Advanced Search

Elisha

35 Reputation

3 Badges

7 years, 253 days
Contact Elisha

MaplePrimes Activity


These are replies submitted by Elisha

@mmcdara Wow, thanks a lot for such...

Elisha 35
February 12 2023
0 0

@mmcdara Wow, thanks a lot for such insight and contribution to knowledge

Help solve this numerically using the gi...

Elisha 35
February 11 2023
0 0

@mmcdara 

Thanks for the input. I have made the necessary corrections but still not giving me the numerical solution that i want. Kindly help with a numerical solution to the system using the given parameters. I need to solve the equation at time 0.1, 0.3, 0.5, 0.7, 0.9, 1.1, 1.3

> 

restart
> 

interface(imaginaryunit = I)

I

 (1)
> 

I

I

 (2)
> 

sqrt(-4)

2*I

 (3)
> 

NULL
> 

Suscep := diff(S(t), t) = theta*epsilon+v__2*S__v(t)-S(t)*lambda-S(t)*(mu+v__1)

diff(S(t), t) = theta*varepsilon+v__2*S__v(t)-S(t)*lambda-S(t)*(mu+v__1)

 (4)
> 

Vacc := diff(S__v(t), t) = (1-theta)*epsilon+v__1*S(t)-(mu+alpha+v__2)*S__v(t)-(1-w)*S__v(t)*lambda
> 

Immun := diff(V(t), t) = alpha*S__v(t)+`ρ__A`*A(t)+(1-k)*`ρ__Q`*Q(t)+`ρ__I`*I(t)-mu*V(t)
> 

Exp := diff(E(t), t) = S(t)*lambda+(1-w)*S__v(t)*lambda-(q__E+delta+mu)*E(t)
> 

Asymp := diff(A(t), t) = delta*a*E(t)-(`ρ__A`+mu)*A(t)+k*`ρ__Q`*Q(t)
> 

Inf := diff(I(t), t) = delta*(1-a)*E(t)-(`ρ__I`+q__I+`δ__I`+mu)*I(t)
> 

Quar := diff(Q(t), t) = q__E*E(t)+q__I*I(t)-(`ρ__Q`+`δ__Q`+mu)*Q(t)
> 

init_conds := S(0) = S_0, S__v(0) = sv0, V(0) = V_0, E(0) = E_0, A(0) = A_0, I(0) = I_0, Q(0) = Q_0

S(0) = S_0, S__v(0) = sv0, V(0) = V_0, E(0) = E_0, A(0) = A_0, I(0) = I_0, Q(0) = Q_0

 (5)
> 

sys := {Asymp, Exp, Immun, Inf, Quar, Suscep, Vacc, init_conds}
> 

``
> 

sol := dsolve(sys, numeric, parameters = [`δ__Q`, `δ__I`, a, k, epsilon, v__1, q__E, q__I, `ρ__A`, `ρ__Q`, `ρ__I`, v__2, alpha, mu, delta, w, lambda, S_0, sv0, V_0, E_0, A_0, I_0, Q_0, theta], method = rkf45)

proc (x_rkf45) local _res, _dat, _vars, _solnproc, _xout, _ndsol, _pars, _n, _i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; if 1 < nargs then error "invalid input: too many arguments" end if; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then _xout := evalf[_EnvDSNumericSaveDigits](x_rkf45) else _xout := evalf(x_rkf45) end if; _dat := Array(1..4, {(1) = proc (_xin) local _xout, _dtbl, _dat, _vmap, _x0, _y0, _val, _dig, _n, _ne, _nd, _nv, _pars, _ini, _par, _i, _j, _k, _src; option `Copyright (c) 2002 by Waterloo Maple Inc. All rights reserved.`; table( [( "complex" ) = false ] ) _xout := _xin; _pars := [delta__Q = delta__Q, delta__I = delta__I, a = a, k = k, varepsilon = varepsilon, v__1 = v__1, q__E = q__E, q__I = q__I, rho__A = rho__A, rho__Q = rho__Q, rho__I = rho__I, v__2 = v__2, alpha = alpha, mu = mu, delta = delta, w = w, lambda = lambda, S_0 = S_0, sv0 = sv0, V_0 = V_0, E_0 = E_0, A_0 = A_0, I_0 = I_0, Q_0 = Q_0, theta = theta]; _dtbl := array( 1 .. 4, [( 1 ) = (array( 1 .. 26, [( 1 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 2 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 3 ) = ([0, 0, 0, Array(1..0, 1..2, {}, datatype = float[8], order = C_order)]), ( 4 ) = (Array(1..63, {(1) = 7, (2) = 7, (3) = 0, (4) = 0, (5) = 25, (6) = 0, (7) = 0, (8) = 0, (9) = 0, (10) = 0, (11) = 0, (12) = 0, (13) = 0, (14) = 0, (15) = 0, (16) = 0, (17) = 0, (18) = 0, (19) = 30000, (20) = 0, (21) = 0, (22) = 1, (23) = 4, (24) = 0, (25) = 1, (26) = 15, (27) = 1, (28) = 0, (29) = 1, (30) = 3, (31) = 3, (32) = 0, (33) = 1, (34) = 0, (35) = 0, (36) = 0, (37) = 0, (38) = 0, (39) = 0, (40) = 0, (41) = 0, (42) = 0, (43) = 1, (44) = 0, (45) = 0, (46) = 0, (47) = 0, (48) = 0, (49) = 0, (50) = 50, (51) = 1, (52) = 0, (53) = 0, (54) = 0, (55) = 0, (56) = 0, (57) = 0, (58) = 0, (59) = 10000, (60) = 0, (61) = 1000, (62) = 0, (63) = 0}, datatype = integer[8])), ( 5 ) = (Array(1..28, {(1) = .0, (2) = 0.10e-5, (3) = .0, (4) = 0.500001e-14, (5) = .0, (6) = .0, (7) = .0, (8) = 0.10e-5, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = 1.0, (14) = .0, (15) = .49999999999999, (16) = .0, (17) = 1.0, (18) = 1.0, (19) = .0, (20) = .0, (21) = 1.0, (22) = 1.0, (23) = .0, (24) = .0, (25) = 0.10e-14, (26) = .0, (27) = .0, (28) = .0}, datatype = float[8], order = C_order)), ( 6 ) = (Array(1..32, {(1) = A_0, (2) = E_0, (3) = I_0, (4) = Q_0, (5) = S_0, (6) = sv0, (7) = V_0, (8) = Float(undefined), (9) = Float(undefined), (10) = Float(undefined), (11) = Float(undefined), (12) = Float(undefined), (13) = Float(undefined), (14) = Float(undefined), (15) = Float(undefined), (16) = Float(undefined), (17) = Float(undefined), (18) = Float(undefined), (19) = Float(undefined), (20) = Float(undefined), (21) = Float(undefined), (22) = Float(undefined), (23) = Float(undefined), (24) = Float(undefined), (25) = Float(undefined), (26) = Float(undefined), (27) = Float(undefined), (28) = Float(undefined), (29) = Float(undefined), (30) = Float(undefined), (31) = Float(undefined), (32) = Float(undefined)})), ( 7 ) = ([Array(1..4, 1..7, {(1, 1) = .0, (1, 2) = .203125, (1, 3) = .3046875, (1, 4) = .75, (1, 5) = .8125, (1, 6) = .40625, (1, 7) = .8125, (2, 1) = 0.6378173828125e-1, (2, 2) = .0, (2, 3) = .279296875, (2, 4) = .27237892150878906, (2, 5) = -0.9686851501464844e-1, (2, 6) = 0.1956939697265625e-1, (2, 7) = .5381584167480469, (3, 1) = 0.31890869140625e-1, (3, 2) = .0, (3, 3) = -.34375, (3, 4) = -.335235595703125, (3, 5) = .2296142578125, (3, 6) = .41748046875, (3, 7) = 11.480712890625, (4, 1) = 0.9710520505905151e-1, (4, 2) = .0, (4, 3) = .40350341796875, (4, 4) = 0.20297467708587646e-1, (4, 5) = -0.6054282188415527e-2, (4, 6) = -0.4770040512084961e-1, (4, 7) = .77858567237854}, datatype = float[8], order = C_order), Array(1..6, 1..6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = 1.0, (2, 1) = .25, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = 1.0, (3, 1) = .1875, (3, 2) = .5625, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = 2.0, (4, 1) = .23583984375, (4, 2) = -.87890625, (4, 3) = .890625, (4, 4) = .0, (4, 5) = .0, (4, 6) = .2681884765625, (5, 1) = .1272735595703125, (5, 2) = -.5009765625, (5, 3) = .44921875, (5, 4) = -0.128936767578125e-1, (5, 5) = .0, (5, 6) = 0.626220703125e-1, (6, 1) = -0.927734375e-1, (6, 2) = .626220703125, (6, 3) = -.4326171875, (6, 4) = .1418304443359375, (6, 5) = -0.861053466796875e-1, (6, 6) = .3131103515625}, datatype = float[8], order = C_order), Array(1..6, {(1) = .0, (2) = .386, (3) = .21, (4) = .63, (5) = 1.0, (6) = 1.0}, datatype = float[8], order = C_order), Array(1..6, {(1) = .25, (2) = -.1043, (3) = .1035, (4) = -0.362e-1, (5) = .0, (6) = .0}, datatype = float[8], order = C_order), Array(1..6, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = 1.544, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = .9466785280815533, (3, 2) = .25570116989825814, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = 3.3148251870684886, (4, 2) = 2.896124015972123, (4, 3) = .9986419139977808, (4, 4) = .0, (4, 5) = .0, (5, 1) = 1.2212245092262748, (5, 2) = 6.019134481287752, (5, 3) = 12.537083329320874, (5, 4) = -.687886036105895, (5, 5) = .0, (6, 1) = 1.2212245092262748, (6, 2) = 6.019134481287752, (6, 3) = 12.537083329320874, (6, 4) = -.687886036105895, (6, 5) = 1.0}, datatype = float[8], order = C_order), Array(1..6, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = -5.6688, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = -2.4300933568337584, (3, 2) = -.20635991570891224, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = -.10735290581452621, (4, 2) = -9.594562251021896, (4, 3) = -20.470286148096154, (4, 4) = .0, (4, 5) = .0, (5, 1) = 7.496443313968615, (5, 2) = -10.246804314641219, (5, 3) = -33.99990352819906, (5, 4) = 11.708908932061595, (5, 5) = .0, (6, 1) = 8.083246795922411, (6, 2) = -7.981132988062785, (6, 3) = -31.52159432874373, (6, 4) = 16.319305431231363, (6, 5) = -6.0588182388340535}, datatype = float[8], order = C_order), Array(1..3, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = 10.126235083446911, (2, 2) = -7.487995877607633, (2, 3) = -34.800918615557414, (2, 4) = -7.9927717075687275, (2, 5) = 1.0251377232956207, (3, 1) = -.6762803392806898, (3, 2) = 6.087714651678606, (3, 3) = 16.43084320892463, (3, 4) = 24.767225114183653, (3, 5) = -6.5943891257167815}, datatype = float[8], order = C_order)]), ( 9 ) = ([Array(1..7, {(1) = .1, (2) = .1, (3) = .1, (4) = .1, (5) = .1, (6) = .1, (7) = .1}, datatype = float[8], order = C_order), Array(1..7, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0}, datatype = float[8], order = C_order), Array(1..7, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0}, datatype = float[8], order = C_order), Array(1..7, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0}, datatype = float[8], order = C_order), Array(1..7, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0}, datatype = float[8], order = C_order), Array(1..7, 1..7, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (1, 7) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (2, 7) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (3, 7) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (4, 7) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (5, 7) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (6, 7) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (7, 5) = .0, (7, 6) = .0, (7, 7) = .0}, datatype = float[8], order = C_order), Array(1..7, 1..7, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (1, 7) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (2, 7) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (3, 7) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (4, 7) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (5, 7) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (6, 7) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (7, 5) = .0, (7, 6) = .0, (7, 7) = .0}, datatype = float[8], order = C_order), Array(1..7, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0}, datatype = float[8], order = C_order), Array(1..7, 1..7, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (1, 7) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (2, 7) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (3, 7) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (4, 7) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (5, 7) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (6, 7) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (7, 5) = .0, (7, 6) = .0, (7, 7) = .0}, datatype = float[8], order = C_order), Array(1..7, 1..6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (7, 5) = .0, (7, 6) = .0}, datatype = float[8], order = C_order), Array(1..7, {(1) = 0, (2) = 0, (3) = 0, (4) = 0, (5) = 0, (6) = 0, (7) = 0}, datatype = integer[8]), Array(1..32, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0, (21) = .0, (22) = .0, (23) = .0, (24) = .0, (25) = .0, (26) = .0, (27) = .0, (28) = .0, (29) = .0, (30) = .0, (31) = .0, (32) = .0}, datatype = float[8], order = C_order), Array(1..32, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0, (21) = .0, (22) = .0, (23) = .0, (24) = .0, (25) = .0, (26) = .0, (27) = .0, (28) = .0, (29) = .0, (30) = .0, (31) = .0, (32) = .0}, datatype = float[8], order = C_order), Array(1..32, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0, (21) = .0, (22) = .0, (23) = .0, (24) = .0, (25) = .0, (26) = .0, (27) = .0, (28) = .0, (29) = .0, (30) = .0, (31) = .0, (32) = .0}, datatype = float[8], order = C_order), Array(1..32, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0, (21) = .0, (22) = .0, (23) = .0, (24) = .0, (25) = .0, (26) = .0, (27) = .0, (28) = .0, (29) = .0, (30) = .0, (31) = .0, (32) = .0}, datatype = float[8], order = C_order), Array(1..7, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0}, datatype = float[8], order = C_order), Array(1..14, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0}, datatype = float[8], order = C_order)]), ( 8 ) = ([Array(1..32, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0, (21) = .0, (22) = .0, (23) = .0, (24) = .0, (25) = .0, (26) = .0, (27) = .0, (28) = .0, (29) = .0, (30) = .0, (31) = .0, (32) = .0}, datatype = float[8], order = C_order), Array(1..32, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0, (21) = .0, (22) = .0, (23) = .0, (24) = .0, (25) = .0, (26) = .0, (27) = .0, (28) = .0, (29) = .0, (30) = .0, (31) = .0, (32) = .0}, datatype = float[8], order = C_order), Array(1..7, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0}, datatype = float[8], order = C_order), 0, 0]), ( 11 ) = (Array(1..6, 0..7, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (1, 7) = .0, (2, 0) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (2, 7) = .0, (3, 0) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (3, 7) = .0, (4, 0) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (4, 7) = .0, (5, 0) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (5, 7) = .0, (6, 0) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (6, 7) = .0}, datatype = float[8], order = C_order)), ( 10 ) = ([proc (N, X, Y, YP) option `[Y[1] = A(t), Y[2] = E(t), Y[3] = I(t), Y[4] = Q(t), Y[5] = S(t), Y[6] = S__v(t), Y[7] = V(t)]`; YP[1] := Y[22]*Y[10]*Y[2]-(Y[16]+Y[21])*Y[1]+Y[11]*Y[17]*Y[4]; YP[2] := Y[5]*Y[24]+(1-Y[23])*Y[6]*Y[24]-(Y[14]+Y[22]+Y[21])*Y[2]; YP[3] := Y[22]*(1-Y[10])*Y[2]-(Y[18]+Y[15]+Y[9]+Y[21])*Y[3]; YP[4] := Y[14]*Y[2]+Y[15]*Y[3]-(Y[17]+Y[8]+Y[21])*Y[4]; YP[5] := Y[32]*Y[12]+Y[19]*Y[6]-Y[5]*Y[24]-Y[5]*(Y[21]+Y[13]); YP[6] := (1-Y[32])*Y[12]+Y[13]*Y[5]-(Y[21]+Y[20]+Y[19])*Y[6]-(1-Y[23])*Y[6]*Y[24]; YP[7] := Y[20]*Y[6]+Y[16]*Y[1]+(1-Y[11])*Y[17]*Y[4]+Y[18]*Y[3]-Y[21]*Y[7]; 0 end proc, -1, 0, 0, 0, 0, 0, 0]), ( 13 ) = (), ( 12 ) = (), ( 15 ) = ("rkf45"), ( 14 ) = ([0, 0]), ( 18 ) = ([]), ( 19 ) = (0), ( 16 ) = ([0, 0, 0, []]), ( 17 ) = ([proc (N, X, Y, YP) option `[Y[1] = A(t), Y[2] = E(t), Y[3] = I(t), Y[4] = Q(t), Y[5] = S(t), Y[6] = S__v(t), Y[7] = V(t)]`; YP[1] := Y[22]*Y[10]*Y[2]-(Y[16]+Y[21])*Y[1]+Y[11]*Y[17]*Y[4]; YP[2] := Y[5]*Y[24]+(1-Y[23])*Y[6]*Y[24]-(Y[14]+Y[22]+Y[21])*Y[2]; YP[3] := Y[22]*(1-Y[10])*Y[2]-(Y[18]+Y[15]+Y[9]+Y[21])*Y[3]; YP[4] := Y[14]*Y[2]+Y[15]*Y[3]-(Y[17]+Y[8]+Y[21])*Y[4]; YP[5] := Y[32]*Y[12]+Y[19]*Y[6]-Y[5]*Y[24]-Y[5]*(Y[21]+Y[13]); YP[6] := (1-Y[32])*Y[12]+Y[13]*Y[5]-(Y[21]+Y[20]+Y[19])*Y[6]-(1-Y[23])*Y[6]*Y[24]; YP[7] := Y[20]*Y[6]+Y[16]*Y[1]+(1-Y[11])*Y[17]*Y[4]+Y[18]*Y[3]-Y[21]*Y[7]; 0 end proc, -1, 0, 0, 0, 0, 0, 0]), ( 22 ) = (0), ( 23 ) = (0), ( 20 ) = ([]), ( 21 ) = (0), ( 26 ) = (Array(1..0, {})), ( 25 ) = (Array(1..0, {})), ( 24 ) = (0) ] )) ] ); _y0 := Array(0..32, {(1) = 0., (2) = A_0, (3) = E_0, (4) = I_0, (5) = Q_0, (6) = S_0, (7) = sv0, (8) = V_0, (9) = undefined, (10) = undefined, (11) = undefined, (12) = undefined, (13) = undefined, (14) = undefined, (15) = undefined, (16) = undefined, (17) = undefined, (18) = undefined, (19) = undefined, (20) = undefined, (21) = undefined, (22) = undefined, (23) = undefined, (24) = undefined, (25) = undefined, (26) = undefined, (27) = undefined, (28) = undefined, (29) = undefined, (30) = undefined, (31) = undefined, (32) = undefined}); _vmap := array( 1 .. 7, [( 1 ) = (1), ( 2 ) = (2), ( 3 ) = (3), ( 4 ) = (4), ( 5 ) = (5), ( 6 ) = (6), ( 7 ) = (7) ] ); _x0 := _dtbl[1][5][5]; _n := _dtbl[1][4][1]; _ne := _dtbl[1][4][3]; _nd := _dtbl[1][4][4]; _nv := _dtbl[1][4][16]; if not type(_xout, 'numeric') then if member(_xout, ["start", "left", "right"]) then if _Env_smart_dsolve_numeric = true or _dtbl[1][4][10] = 1 then if _xout = "left" then if type(_dtbl[2], 'table') then return _dtbl[2][5][1] end if elif _xout = "right" then if type(_dtbl[3], 'table') then return _dtbl[3][5][1] end if end if end if; return _dtbl[1][5][5] elif _xout = "method" then return _dtbl[1][15] elif _xout = "storage" then return evalb(_dtbl[1][4][10] = 1) elif _xout = "leftdata" then if not type(_dtbl[2], 'array') then return NULL else return eval(_dtbl[2]) end if elif _xout = "rightdata" then if not type(_dtbl[3], 'array') then return NULL else return eval(_dtbl[3]) end if elif _xout = "enginedata" then return eval(_dtbl[1]) elif _xout = "enginereset" then _dtbl[2] := evaln(_dtbl[2]); _dtbl[3] := evaln(_dtbl[3]); return NULL elif _xout = "initial" then return procname(_y0[0]) elif _xout = "laxtol" then return _dtbl[`if`(member(_dtbl[4], {2, 3}), _dtbl[4], 1)][5][18] elif _xout = "numfun" then return `if`(member(_dtbl[4], {2, 3}), _dtbl[_dtbl[4]][4][18], 0) elif _xout = "parameters" then return [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] elif _xout = "initial_and_parameters" then return procname(_y0[0]), [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] elif _xout = "last" then if _dtbl[4] <> 2 and _dtbl[4] <> 3 or _x0-_dtbl[_dtbl[4]][5][1] = 0. then error "no information is available on last computed point" else _xout := _dtbl[_dtbl[4]][5][1] end if elif _xout = "function" then if _dtbl[1][4][33]-2. = 0 then return eval(_dtbl[1][10], 1) else return eval(_dtbl[1][10][1], 1) end if elif _xout = "map" then return copy(_vmap) elif type(_xin, `=`) and type(rhs(_xin), 'list') and member(lhs(_xin), {"initial", "parameters", "initial_and_parameters"}) then _ini, _par := [], []; if lhs(_xin) = "initial" then _ini := rhs(_xin) elif lhs(_xin) = "parameters" then _par := rhs(_xin) elif select(type, rhs(_xin), `=`) <> [] then _par, _ini := selectremove(type, rhs(_xin), `=`) elif nops(rhs(_xin)) < nops(_pars)+1 then error "insufficient data for specification of initial and parameters" else _par := rhs(_xin)[-nops(_pars) .. -1]; _ini := rhs(_xin)[1 .. -nops(_pars)-1] end if; _xout := lhs(_xout); if _par <> [] then `dsolve/numeric/process_parameters`(_n, _pars, _par, _y0) end if; if _ini <> [] then `dsolve/numeric/process_initial`(_n-_ne, _ini, _y0, _pars, _vmap) end if; `dsolve/numeric/SC/reinitialize`(_dtbl, _y0, _n, procname, _pars); if _Env_smart_dsolve_numeric = true and type(_y0[0], 'numeric') and _dtbl[1][4][10] <> 1 then procname("right") := _y0[0]; procname("left") := _y0[0] end if; if _xout = "initial" then return [_y0[0], seq(_y0[_vmap[_i]], _i = 1 .. _n-_ne)] elif _xout = "parameters" then return [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] else return [_y0[0], seq(_y0[_vmap[_i]], _i = 1 .. _n-_ne)], [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] end if elif _xin = "eventstop" then if _nv = 0 then error "this solution has no events" end if; _i := _dtbl[4]; if _i <> 2 and _i <> 3 then return 0 end if; if _dtbl[_i][4][10] = 1 and assigned(_dtbl[5-_i]) and _dtbl[_i][4][9] < 100 and 100 <= _dtbl[5-_i][4][9] then _i := 5-_i; _dtbl[4] := _i; _j := round(_dtbl[_i][4][17]); return round(_dtbl[_i][3][1][_j, 1]) elif 100 <= _dtbl[_i][4][9] then _j := round(_dtbl[_i][4][17]); return round(_dtbl[_i][3][1][_j, 1]) else return 0 end if elif _xin = "eventstatus" then if _nv = 0 then error "this solution has no events" end if; _i := [selectremove(proc (a) options operator, arrow; _dtbl[1][3][1][a, 7] = 1 end proc, {seq(_j, _j = 1 .. round(_dtbl[1][3][1][_nv+1, 1]))})]; return ':-enabled' = _i[1], ':-disabled' = _i[2] elif _xin = "eventclear" then if _nv = 0 then error "this solution has no events" end if; _i := _dtbl[4]; if _i <> 2 and _i <> 3 then error "no events to clear" end if; if _dtbl[_i][4][10] = 1 and assigned(_dtbl[5-_i]) and _dtbl[_i][4][9] < 100 and 100 < _dtbl[5-_i][4][9] then _dtbl[4] := 5-_i; _i := 5-_i end if; if _dtbl[_i][4][9] < 100 then error "no events to clear" elif _nv < _dtbl[_i][4][9]-100 then error "event error condition cannot be cleared" else _j := _dtbl[_i][4][9]-100; if irem(round(_dtbl[_i][3][1][_j, 4]), 2) = 1 then error "retriggerable events cannot be cleared" end if; _j := round(_dtbl[_i][3][1][_j, 1]); for _k to _nv do if _dtbl[_i][3][1][_k, 1] = _j then if _dtbl[_i][3][1][_k, 2] = 3 then error "range events cannot be cleared" end if; _dtbl[_i][3][1][_k, 8] := _dtbl[_i][3][1][_nv+1, 8] end if end do; _dtbl[_i][4][17] := 0; _dtbl[_i][4][9] := 0; if _dtbl[1][4][10] = 1 then if _i = 2 then try procname(procname("left")) catch: end try else try procname(procname("right")) catch: end try end if end if end if; return elif type(_xin, `=`) and member(lhs(_xin), {"eventdisable", "eventenable"}) then if _nv = 0 then error "this solution has no events" end if; if type(rhs(_xin), {('list')('posint'), ('set')('posint')}) then _i := {op(rhs(_xin))} elif type(rhs(_xin), 'posint') then _i := {rhs(_xin)} else error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; if select(proc (a) options operator, arrow; _nv < a end proc, _i) <> {} then error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; _k := {}; for _j to _nv do if member(round(_dtbl[1][3][1][_j, 1]), _i) then _k := `union`(_k, {_j}) end if end do; _i := _k; if lhs(_xin) = "eventdisable" then _dtbl[4] := 0; _j := [evalb(assigned(_dtbl[2]) and member(_dtbl[2][4][17], _i)), evalb(assigned(_dtbl[3]) and member(_dtbl[3][4][17], _i))]; for _k in _i do _dtbl[1][3][1][_k, 7] := 0; if assigned(_dtbl[2]) then _dtbl[2][3][1][_k, 7] := 0 end if; if assigned(_dtbl[3]) then _dtbl[3][3][1][_k, 7] := 0 end if end do; if _j[1] then for _k to _nv+1 do if _k <= _nv and not type(_dtbl[2][3][4][_k, 1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to defined init `, _dtbl[2][3][4][_k, 1]); _dtbl[2][3][1][_k, 8] := _dtbl[2][3][4][_k, 1] elif _dtbl[2][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[2][3][1][_k, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to rate hysteresis init `, _dtbl[2][5][24]); _dtbl[2][3][1][_k, 8] := _dtbl[2][5][24] elif _dtbl[2][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[2][3][1][_k, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to initial init `, _x0); _dtbl[2][3][1][_k, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to fireinitial init `, _x0-1); _dtbl[2][3][1][_k, 8] := _x0-1 end if end do; _dtbl[2][4][17] := 0; _dtbl[2][4][9] := 0; if _dtbl[1][4][10] = 1 then procname(procname("left")) end if end if; if _j[2] then for _k to _nv+1 do if _k <= _nv and not type(_dtbl[3][3][4][_k, 2], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to defined init `, _dtbl[3][3][4][_k, 2]); _dtbl[3][3][1][_k, 8] := _dtbl[3][3][4][_k, 2] elif _dtbl[3][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[3][3][1][_k, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to rate hysteresis init `, _dtbl[3][5][24]); _dtbl[3][3][1][_k, 8] := _dtbl[3][5][24] elif _dtbl[3][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[3][3][1][_k, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to initial init `, _x0); _dtbl[3][3][1][_k, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to fireinitial init `, _x0+1); _dtbl[3][3][1][_k, 8] := _x0+1 end if end do; _dtbl[3][4][17] := 0; _dtbl[3][4][9] := 0; if _dtbl[1][4][10] = 1 then procname(procname("right")) end if end if else for _k in _i do _dtbl[1][3][1][_k, 7] := 1 end do; _dtbl[2] := evaln(_dtbl[2]); _dtbl[3] := evaln(_dtbl[3]); _dtbl[4] := 0; if _dtbl[1][4][10] = 1 then if _x0 <= procname("right") then try procname(procname("right")) catch: end try end if; if procname("left") <= _x0 then try procname(procname("left")) catch: end try end if end if end if; return elif type(_xin, `=`) and lhs(_xin) = "eventfired" then if not type(rhs(_xin), 'list') then error "'eventfired' must be specified as a list" end if; if _nv = 0 then error "this solution has no events" end if; if _dtbl[4] <> 2 and _dtbl[4] <> 3 then error "'direction' must be set prior to calling/setting 'eventfired'" end if; _i := _dtbl[4]; _val := NULL; if not assigned(_EnvEventRetriggerWarned) then _EnvEventRetriggerWarned := false end if; for _k in rhs(_xin) do if type(_k, 'integer') then _src := _k elif type(_k, 'integer' = 'anything') and type(evalf(rhs(_k)), 'numeric') then _k := lhs(_k) = evalf[max(Digits, 18)](rhs(_k)); _src := lhs(_k) else error "'eventfired' entry is not valid: %1", _k end if; if _src < 1 or round(_dtbl[1][3][1][_nv+1, 1]) < _src then error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; _src := {seq(`if`(_dtbl[1][3][1][_j, 1]-_src = 0., _j, NULL), _j = 1 .. _nv)}; if nops(_src) <> 1 then error "'eventfired' can only be set/queried for root-finding events and time/interval events" end if; _src := _src[1]; if _dtbl[1][3][1][_src, 2] <> 0. and _dtbl[1][3][1][_src, 2]-2. <> 0. then error "'eventfired' can only be set/queried for root-finding events and time/interval events" elif irem(round(_dtbl[1][3][1][_src, 4]), 2) = 1 then if _EnvEventRetriggerWarned = false then WARNING(`'eventfired' has no effect on events that retrigger`) end if; _EnvEventRetriggerWarned := true end if; if _dtbl[_i][3][1][_src, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_src, 4]), 32), 2) = 1 then _val := _val, undefined elif type(_dtbl[_i][3][4][_src, _i-1], 'undefined') or _i = 2 and _dtbl[2][3][1][_src, 8] < _dtbl[2][3][4][_src, 1] or _i = 3 and _dtbl[3][3][4][_src, 2] < _dtbl[3][3][1][_src, 8] then _val := _val, _dtbl[_i][3][1][_src, 8] else _val := _val, _dtbl[_i][3][4][_src, _i-1] end if; if type(_k, `=`) then if _dtbl[_i][3][1][_src, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_src, 4]), 32), 2) = 1 then error "cannot set event code for a rate hysteresis event" end if; userinfo(3, {'events', 'eventreset'}, `manual set event code `, _src, ` to value `, rhs(_k)); _dtbl[_i][3][1][_src, 8] := rhs(_k); _dtbl[_i][3][4][_src, _i-1] := rhs(_k) end if end do; return [_val] elif type(_xin, `=`) and lhs(_xin) = "direction" then if not member(rhs(_xin), {-1, 1, ':-left', ':-right'}) then error "'direction' must be specified as either '1' or 'right' (positive) or '-1' or 'left' (negative)" end if; _src := `if`(_dtbl[4] = 2, -1, `if`(_dtbl[4] = 3, 1, undefined)); _i := `if`(member(rhs(_xin), {1, ':-right'}), 3, 2); _dtbl[4] := _i; _dtbl[_i] := `dsolve/numeric/SC/IVPdcopy`(_dtbl[1], `if`(assigned(_dtbl[_i]), _dtbl[_i], NULL)); if 0 < _nv then for _j to _nv+1 do if _j <= _nv and not type(_dtbl[_i][3][4][_j, _i-1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to defined init `, _dtbl[_i][3][4][_j, _i-1]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][3][4][_j, _i-1] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to rate hysteresis init `, _dtbl[_i][5][24]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][5][24] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to initial init `, _x0); _dtbl[_i][3][1][_j, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to fireinitial init `, _x0-2*_i+5.0); _dtbl[_i][3][1][_j, 8] := _x0-2*_i+5.0 end if end do end if; return _src elif _xin = "eventcount" then if _dtbl[1][3][1] = 0 or _dtbl[4] <> 2 and _dtbl[4] <> 3 then return 0 else return round(_dtbl[_dtbl[4]][3][1][_nv+1, 12]) end if else return "procname" end if end if; if _xout = _x0 then return [_x0, seq(evalf(_dtbl[1][6][_vmap[_i]]), _i = 1 .. _n-_ne)] end if; _i := `if`(_x0 <= _xout, 3, 2); if _xin = "last" and 0 < _dtbl[_i][4][9] and _dtbl[_i][4][9] < 100 then _dat := eval(_dtbl[_i], 2); _j := _dat[4][20]; return [_dat[11][_j, 0], seq(_dat[11][_j, _vmap[_i]], _i = 1 .. _n-_ne-_nd), seq(_dat[8][1][_vmap[_i]], _i = _n-_ne-_nd+1 .. _n-_ne)] end if; if not type(_dtbl[_i], 'array') then _dtbl[_i] := `dsolve/numeric/SC/IVPdcopy`(_dtbl[1], `if`(assigned(_dtbl[_i]), _dtbl[_i], NULL)); if 0 < _nv then for _j to _nv+1 do if _j <= _nv and not type(_dtbl[_i][3][4][_j, _i-1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to defined init `, _dtbl[_i][3][4][_j, _i-1]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][3][4][_j, _i-1] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to rate hysteresis init `, _dtbl[_i][5][24]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][5][24] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to initial init `, _x0); _dtbl[_i][3][1][_j, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to fireinitial init `, _x0-2*_i+5.0); _dtbl[_i][3][1][_j, 8] := _x0-2*_i+5.0 end if end do end if end if; if _xin <> "last" then if 0 < 0 then if `dsolve/numeric/checkglobals`(op(_dtbl[1][14]), _pars, _n, _y0) then `dsolve/numeric/SC/reinitialize`(_dtbl, _y0, _n, procname, _pars, _i) end if end if; if _dtbl[1][4][7] = 0 then error "parameters must be initialized before solution can be computed" end if end if; _dat := eval(_dtbl[_i], 2); _dtbl[4] := _i; try _src := `dsolve/numeric/SC/IVPrun`(_dat, _xout) catch: userinfo(2, `dsolve/debug`, print(`Exception in solnproc:`, [lastexception][2 .. -1])); error end try; if _dat[17] <> _dtbl[1][17] then _dtbl[1][17] := _dat[17]; _dtbl[1][10] := _dat[10] end if; if _src = 0 and 100 < _dat[4][9] then _val := _dat[3][1][_nv+1, 8] else _val := _dat[11][_dat[4][20], 0] end if; if _src <> 0 or _dat[4][9] <= 0 then _dtbl[1][5][1] := _xout else _dtbl[1][5][1] := _val end if; if _i = 3 and _val < _xout then Rounding := -infinity; if _dat[4][9] = 1 then error "cannot evaluate the solution further right of %1, probably a singularity", evalf[8](_val) elif _dat[4][9] = 2 then error "cannot evaluate the solution further right of %1, maxfun limit exceeded (see ?dsolve,maxfun for details)", evalf[8](_val) elif _dat[4][9] = 3 then if _dat[4][25] = 3 then error "cannot evaluate the solution past the initial point, problem may be initially singular or improperly set up" else error "cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up" end if elif _dat[4][9] = 4 then error "cannot evaluate the solution further right of %1, accuracy goal cannot be achieved with specified 'minstep'", evalf[8](_val) elif _dat[4][9] = 5 then error "cannot evaluate the solution further right of %1, too many step failures, tolerances may be too loose for problem", evalf[8](_val) elif _dat[4][9] = 6 then error "cannot evaluate the solution further right of %1, cannot downgrade delay storage for problems with delay derivative order > 1, try increasing delaypts", evalf[8](_val) elif _dat[4][9] = 10 then error "cannot evaluate the solution further right of %1, interrupt requested", evalf[8](_val) elif 100 < _dat[4][9] then if _dat[4][9]-100 = _nv+1 then error "constraint projection failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+2 then error "index-1 and derivative evaluation failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+3 then error "maximum number of event iterations reached (%1) at t=%2", round(_dat[3][1][_nv+1, 3]), evalf[8](_val) else if _Env_dsolve_nowarnstop <> true then `dsolve/numeric/warning`(StringTools:-FormatMessage("cannot evaluate the solution further right of %1, event #%2 triggered a halt", evalf[8](_val), round(_dat[3][1][_dat[4][9]-100, 1]))) end if; Rounding := 'nearest'; _xout := _val end if else error "cannot evaluate the solution further right of %1", evalf[8](_val) end if elif _i = 2 and _xout < _val then Rounding := infinity; if _dat[4][9] = 1 then error "cannot evaluate the solution further left of %1, probably a singularity", evalf[8](_val) elif _dat[4][9] = 2 then error "cannot evaluate the solution further left of %1, maxfun limit exceeded (see ?dsolve,maxfun for details)", evalf[8](_val) elif _dat[4][9] = 3 then if _dat[4][25] = 3 then error "cannot evaluate the solution past the initial point, problem may be initially singular or improperly set up" else error "cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up" end if elif _dat[4][9] = 4 then error "cannot evaluate the solution further left of %1, accuracy goal cannot be achieved with specified 'minstep'", evalf[8](_val) elif _dat[4][9] = 5 then error "cannot evaluate the solution further left of %1, too many step failures, tolerances may be too loose for problem", evalf[8](_val) elif _dat[4][9] = 6 then error "cannot evaluate the solution further left of %1, cannot downgrade delay storage for problems with delay derivative order > 1, try increasing delaypts", evalf[8](_val) elif _dat[4][9] = 10 then error "cannot evaluate the solution further right of %1, interrupt requested", evalf[8](_val) elif 100 < _dat[4][9] then if _dat[4][9]-100 = _nv+1 then error "constraint projection failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+2 then error "index-1 and derivative evaluation failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+3 then error "maximum number of event iterations reached (%1) at t=%2", round(_dat[3][1][_nv+1, 3]), evalf[8](_val) else if _Env_dsolve_nowarnstop <> true then `dsolve/numeric/warning`(StringTools:-FormatMessage("cannot evaluate the solution further left of %1, event #%2 triggered a halt", evalf[8](_val), round(_dat[3][1][_dat[4][9]-100, 1]))) end if; Rounding := 'nearest'; _xout := _val end if else error "cannot evaluate the solution further left of %1", evalf[8](_val) end if end if; if _EnvInFsolve = true then _dig := _dat[4][26]; if type(_EnvDSNumericSaveDigits, 'posint') then _dat[4][26] := _EnvDSNumericSaveDigits else _dat[4][26] := Digits end if; _Env_dsolve_SC_native := true; if _dat[4][25] = 1 then _i := 1; _dat[4][25] := 2 else _i := _dat[4][25] end if; _val := `dsolve/numeric/SC/IVPval`(_dat, _xout, _src); _dat[4][25] := _i; _dat[4][26] := _dig; [_xout, seq(_val[_vmap[_i]], _i = 1 .. _n-_ne)] else Digits := _dat[4][26]; _val := `dsolve/numeric/SC/IVPval`(eval(_dat, 2), _xout, _src); [_xout, seq(_val[_vmap[_i]], _i = 1 .. _n-_ne)] end if end proc, (2) = Array(0..0, {}), (3) = [t, A(t), E(t), I(t), Q(t), S(t), S__v(t), V(t)], (4) = [delta__Q = delta__Q, delta__I = delta__I, a = a, k = k, varepsilon = varepsilon, v__1 = v__1, q__E = q__E, q__I = q__I, rho__A = rho__A, rho__Q = rho__Q, rho__I = rho__I, v__2 = v__2, alpha = alpha, mu = mu, delta = delta, w = w, lambda = lambda, S_0 = S_0, sv0 = sv0, V_0 = V_0, E_0 = E_0, A_0 = A_0, I_0 = I_0, Q_0 = Q_0, theta = theta]}); _vars := _dat[3]; _pars := map(rhs, _dat[4]); _n := nops(_vars)-1; _solnproc := _dat[1]; if not type(_xout, 'numeric') then if member(x_rkf45, ["start", 'start', "method", 'method', "left", 'left', "right", 'right', "leftdata", "rightdata", "enginedata", "eventstop", 'eventstop', "eventclear", 'eventclear', "eventstatus", 'eventstatus', "eventcount", 'eventcount', "laxtol", 'laxtol', "numfun", 'numfun', NULL]) then _res := _solnproc(convert(x_rkf45, 'string')); if 1 < nops([_res]) then return _res elif type(_res, 'array') then return eval(_res, 1) elif _res <> "procname" then return _res end if elif member(x_rkf45, ["last", 'last', "initial", 'initial', "parameters", 'parameters', "initial_and_parameters", 'initial_and_parameters', NULL]) then _xout := convert(x_rkf45, 'string'); _res := _solnproc(_xout); if _xout = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] elif _xout = "initial_and_parameters" then return [seq(_vars[_i+1] = [_res][1][_i+1], _i = 0 .. _n), seq(_pars[_i] = [_res][2][_i], _i = 1 .. nops(_pars))] else return [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] end if elif type(_xout, `=`) and member(lhs(_xout), ["initial", 'initial', "parameters", 'parameters', "initial_and_parameters", 'initial_and_parameters', NULL]) then _xout := convert(lhs(x_rkf45), 'string') = rhs(x_rkf45); if type(rhs(_xout), 'list') then _res := _solnproc(_xout) else error "initial and/or parameter values must be specified in a list" end if; if lhs(_xout) = "initial" then return [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] elif lhs(_xout) = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] else return [seq(_vars[_i+1] = [_res][1][_i+1], _i = 0 .. _n), seq(_pars[_i] = [_res][2][_i], _i = 1 .. nops(_pars))] end if elif type(_xout, `=`) and member(lhs(_xout), ["eventdisable", 'eventdisable', "eventenable", 'eventenable', "eventfired", 'eventfired', "direction", 'direction', NULL]) then return _solnproc(convert(lhs(x_rkf45), 'string') = rhs(x_rkf45)) elif _xout = "solnprocedure" then return eval(_solnproc) elif _xout = "sysvars" then return _vars end if; if procname <> unknown then return ('procname')(x_rkf45) else _ndsol := 1; _ndsol := _ndsol; _ndsol := pointto(_dat[2][0]); return ('_ndsol')(x_rkf45) end if end if; try _res := _solnproc(_xout); [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] catch: error end try end proc

 (6)
> 

sol(parameters = [delta = .125, `&delta;__Q` = 0.6847e-3, epsilon = .464360344, `&delta;__I` = 0.2230e-8, a = .6255, q[E] = 0.18113e-3, k = .15, v__1 = 0.5e-1, v__2 = 0.6e-1, `&rho;__Q` = 0.815e-1, `&rho;__A` = .1, `&rho;__I` = 0.666666e-1, q__I = 0.1923e-2, alpha = .4, w = .5925, mu = 0.464360344e-4, lambda = 0.1598643e-7, S_0 = 1.0, S__v*_0 = 0.6e-4, V_0 = 0.35e-4, E_0 = 0.5e-4, I_0 = 0.32e-4, A_0 = 0.15e-4, Q_0 = 0.1e-4, theta = 0.5e-2])

Error, (in dsolve/numeric/process_parameters) 'parameters' must be specified as a list of numeric values

  
> 

Evaluate*the*system*at*t = 2
> 

sol(2)

sol(2)

 (7)
> 

sol(1)

sol(1)

 (8)
> 

sol(.1)

sol(.1)

 (9)
> 

sol(.3)

sol(.3)

 (10)
> 

sol(.5)

sol(.5)

 (11)
> 

sol(.7)

sol(.7)

 (12)
> 

sol(.9)

sol(.9)

 (13)
> 

sol(1.1)

sol(1.1)

 (14)
> 

sol(1.3)

sol(1.3)

 (15)
> 

sol(1.5)

sol(1.5)

 (16)
> 

``

Download Covid19_Simulation2.mw

Error Encountered...

Elisha 35
January 17 2018
0 0

@Preben Alsholm Thanks alot, I worked.

error still encountered...

Elisha 35
January 12 2018
0 0

@Preben Alsholm I did just as you advised and Maple brought up this error:


 

NULL

> 

restart
> 

ode := diff(s(t), t) = (1-phi)*epsilon+(1-rho)*a+(1-f)*alpha*v(t)-(lambda+theta[1]+a+epsilon)*s(t)*(diff(v(t), t)) and (1-phi)*epsilon+(1-rho)*a+(1-f)*alpha*v(t)-(lambda+theta[1]+a+epsilon)*s(t)*(diff(v(t), t)) = phi*epsilon+rho*a+theta[1]*s(t)-((1-f)*alpha+f*theta[2]+a+epsilon)*v(t)*(diff(v(t), t)) and phi*epsilon+rho*a+theta[1]*s(t)-((1-f)*alpha+f*theta[2]+a+epsilon)*v(t)*(diff(v(t), t)) = phi*epsilon+rho*a+theta[1]*s(t)-((1-f)*alpha+f*theta[2]+a+epsilon)*v(t)*(diff(e(t), t)) and phi*epsilon+rho*a+theta[1]*s(t)-((1-f)*alpha+f*theta[2]+a+epsilon)*v(t)*(diff(e(t), t)) = lambda*s(t)-(delta+a+epsilon)*e(t)*(diff(i(t), t)) and lambda*s(t)-(delta+a+epsilon)*e(t)*(diff(i(t), t)) = delta*e(t)-(eta+a+epsilon)*i(t)

false

 (1)
> 

restart
> 

``

NULL

> 

v(0) := .4;

.4

 (2)
> 

NULL
> 

s(0) := 0.6e-1;

0.6e-1

 (3)
> 

e(0) := .24;

.24

 (4)
> 

i(0) := .17;

.17

 (5)
> 

r(0) := .13;

.13

 (6)
> 

c := 0.4e-1;

0.4e-1

 (7)
> 

f := .4;

.4

 (8)
> 

beta := .2;

.2

 (9)
> 

epsilon := .8;

.8

 (10)
> 

theta[1] := .1;

.1

 (11)
> 

theta[2] := .3;

.3

 (12)
> 

alpha := .9;

.9

 (13)
> 

rho := .7;

.7

 (14)
> 

eta := .99;

.99

 (15)
> 

delta := .3;

.3

 (16)
> 

a := 0.4e-1;

0.4e-1

 (17)
> 

phi := 1;

1

 (18)
> 

NULL
> 

ode1 := diff(s(t), t) = (1-phi)*epsilon+(1-rho)*a+(1-f)*alpha*v(t)-(lambda+theta[1]+a+epsilon)*s(t);

diff(s(t), t) = 0.12e-1+.54*v(t)-(lambda+.94)*s(t)

 (19)
> 

ode2 := diff(v(t), t) = phi*epsilon+rho*a+theta[1]*s(t)-((1-f)*alpha+f*theta[2]+a+epsilon)*v(t);

diff(v(t), t) = .828+.1*s(t)-1.50*v(t)

 (20)
> 

ode3 := diff(e(t), t) = lambda*s(t)-(delta+a+epsilon)*e(t);

diff(e(t), t) = lambda*s(t)-1.14*e(t)

 (21)
> 

ode4 := diff(i(t), t) = delta*e(t)-(eta+a+epsilon)*i(t);

diff(i(t), t) = .3*e(t)-1.83*i(t)

 (22)
> 

ode5 := diff(r(t), t) = eta*i(t)+f*theta[2]*v(t)-(a+epsilon)*r(t);

diff(r(t), t) = .99*i(t)+.12*v(t)-.84*r(t)

 (23)
> 

h := .1:
> 

resRK4 := dsolve({ode1, ode2, ode3, ode4, ode5, e(0) = .24, i(0) = .17, r(0) = .13, s(0) = 0.6e-1, v(0) = .4}, numeric, method = classical[rk4], stepsize = h, output = Array([seq(h*i, i = 0 .. 20)]))

Error, (in dsolve/numeric/process_input) invalid specification of initial conditions, got {0.6e-1 = 0.6e-1, .13 = .13, .17 = .17, .24 = .24, .4 = .4}

  
> 

NULL

NULL


Pls help me out.

Download ODE2_WORK.mw

Is my whole code correct?...

Elisha 35
January 10 2018
0 0

@acer Apart from spelling error of stepsize as stepsise, is the entire code going to run correctly? I on track sir? required result? Am away from my Maple software now

Error Encountered...

Elisha 35
January 10 2018
0 0

@Preben Alsholm I followed your example and tried solving my work. Pls find below the error encountered.


 

``

> 

restart
> 

ode := diff(s(t), t) = (1-phi)*epsilon+(1-rho)*a+(1-f)*alpha*v(t)-(lambda+theta[1]+a+epsilon)*s(t)*(diff(v(t), t)) and (1-phi)*epsilon+(1-rho)*a+(1-f)*alpha*v(t)-(lambda+theta[1]+a+epsilon)*s(t)*(diff(v(t), t)) = phi*epsilon+rho*a+theta[1]*s(t)-((1-f)*alpha+f*theta[2]+a+epsilon)*v(t)*(diff(v(t), t)) and phi*epsilon+rho*a+theta[1]*s(t)-((1-f)*alpha+f*theta[2]+a+epsilon)*v(t)*(diff(v(t), t)) = phi*epsilon+rho*a+theta[1]*s(t)-((1-f)*alpha+f*theta[2]+a+epsilon)*v(t)*(diff(e(t), t)) and phi*epsilon+rho*a+theta[1]*s(t)-((1-f)*alpha+f*theta[2]+a+epsilon)*v(t)*(diff(e(t), t)) = lambda*s(t)-(delta+a+epsilon)*e(t)*(diff(i(t), t)) and lambda*s(t)-(delta+a+epsilon)*e(t)*(diff(i(t), t)) = delta*e(t)-(eta+a+epsilon)*i(t)

false

 (1)
> 

restart
> 

ode1 := diff(s(t), t) = (1-phi)*epsilon+(1-rho)*a+(1-f)*alpha*v(t)-(lambda+theta[1]+a+epsilon)*s(t);

diff(s(t), t) = (1-phi)*epsilon+(1-rho)*a+(1-f)*alpha*v(t)-(lambda+theta[1]+a+epsilon)*s(t)

 (2)
> 

ode2 := diff(v(t), t) = phi*epsilon+rho*a+theta[1]*s(t)-((1-f)*alpha+f*theta[2]+a+epsilon)*v(t);

diff(v(t), t) = phi*epsilon+rho*a+theta[1]*s(t)-((1-f)*alpha+f*theta[2]+a+epsilon)*v(t)

 (3)
> 

ode3 := diff(e(t), t) = lambda*s(t)-(delta+a+epsilon)*e(t);

diff(e(t), t) = lambda*s(t)-(delta+a+epsilon)*e(t)

 (4)
> 

ode4 := diff(i(t), t) = delta*e(t)-(eta+a+epsilon)*i(t);

diff(i(t), t) = delta*e(t)-(eta+a+epsilon)*i(t)

 (5)
> 

ode5 := diff(r(t), t) = eta*i(t)+f*theta[2]*v(t)-(a+epsilon)*r(t);

diff(r(t), t) = eta*i(t)+f*theta[2]*v(t)-(a+epsilon)*r(t)

 (6)
> 

h := .1:
> 

resRK4 := dsolve({ode1, ode2, ode3, ode4, ode5, s(0) = 0.6e-1}, numeric, method = classical[rk4], stepsise = h, output = Array([seq(h*i, i = 0 .. 20)]))

Warning, The use of global variables in numerical ODE problems is deprecated, and will be removed in a future release. Use the 'parameters' argument instead (see ?dsolve,numeric,parameters)

  

Error, (in dsolve/numeric/an_args/classical) classical keyword was stepsise, optional keyword must be one of 'corrections', 'stepsize', 'initial', 'maxfun', 'output', 'procedure', 'procvars', 'start', 'number', 'startinit', 'implicit', 'optimize', 'complex'

  
> 

``

``


 

Download ODE2_WORK.mw

Use of RK4...

Elisha 35
January 06 2018
0 0

@Carl Love Carl, I have used RKF45 as advised, and have obtained my result. I still want to see what RK4 solution will look like. How do i use dsolve(...,numeric, method=classical[RK4]); for the equation below: an examplary guide will do.


 

``

> 

ODE*equations

ODE*equations

 (1)
> 

diff(s(t), t) = (1-phi)*epsilon+(1-rho)*a+(1-f)*alpha*v(t)-(lambda+theta[1]+a+epsilon)*s(t)
> 

diff(v(t), t) = phi*epsilon+rho*a+theta[1]*s(t)-((1-f)*alpha+f*theta[2]+a+epsilon)*v(t)
> 

diff(e(t), t) = lambda*s(t)-(delta+a+epsilon)*e(t)
> 

NULL
> 

diff(r(t), t) = eta*i(t)+v(t)*f*theta[2]-(a+epsilon)*r(t)
> 

``
> 

``
> 

My*parameters

My*parameters

 (2)
> 

v(0) := .4

.4

 (3)
> 

NULL
> 

s(0) := 0.6e-1

0.6e-1

 (4)
> 

e[0] := .24

.24

 (5)
> 

i[0] := .17

.17

 (6)
> 

r[0] := .13

.13

 (7)
> 

c := 0.4e-1

0.4e-1

 (8)
> 

f := .4

.4

 (9)
> 

beta := .2

.2

 (10)
> 

epsilon := .8

.8

 (11)
> 

theta[1] := .1

.1

 (12)
> 

theta[2] := .3

.3

 (13)
> 

alpha := .9

.9

 (14)
> 

rho := .7

.7

 (15)
> 

eta := .99

.99

 (16)
> 

delta := .3

.3

 (17)
> 

a := 0.4e-1

0.4e-1

 (18)
> 

phi := 1
> 

``
> 

``

``


 

Download ODE_EQNS.mw

Is the Solution for RKF45 thesame as Exa...

Elisha 35
January 05 2018
0 0

@Carl Love The Exact solution I got is the same as that of RKF45. So I could not do any comparison? Is Exact solution on Maple same as solution of RKF45? Pls help with example on how the two different solution can be realised.

Only Two out of my Three Graphs is Displ...

Elisha 35
January 05 2018
0 0

@gkokovidis Happy new year. I did just as you advised. I reduced the thickness to the least I could get but still having same issue. The essence of my comparison could be defeated if only two out of three graphs are visible. kindly assist and advised to get me out of this mess. I look forward to your prompt response

Regards.

Only Two out of my Three Graphs is Displ...

Elisha 35
December 30 2017
0 0

@gkokovidis  I have plotted my graphs as advised but only two out of my three graphs is dispalyed. I checked all my commands but could not find the reason why this. Pls what could be the cause? find what i did below for your guide:


 

NULL

NULL

> 

restart; with(plots)
> 

Data := [[.1, 0.769540597e-1, .1477783335, .1393069312, 0.763361154e-1, .1477867626, .1393072151, 0.763361266e-1, .1477867830, .1393071934], [.3, .1093424148, .1120401102, .1509302274, .1072278404, .1121142033, .1509369166, .1072278479, .1121142168, .1509369024], [.5, .1392030568, 0.853083077e-1, .1558066181, .1353291378, 0.855066806e-1, .1558355785, .1353291558, 0.8550671332e-1, .1558355439], [.7, .1662374563, 0.652194693e-1, .1562235596, .1604342222, 0.655908735e-1, .1562974878, .1604342352, 0.6559089617e-1, .1562974637], [.9, .1903821623, 0.500537619e-1, .1537887672, .1825594352, 0.506356391e-1, .1539346707, .1825594528, 0.5063567192e-1, .1539346352], [1.1, .2117168860, 0.385555127e-1, .1496220815, .2018541863, 0.393727175e-1, .1498707561, .2018542024, 0.3937274753e-1, .1498707234], [1.3, .2303874000, 0.298096396e-1, .1444864012, .2185409755, 0.308687065e-1, .1448804021, .2185409880, 0.3086872986e-1, .1448803765], [1.5, .2465077820, 0.231661161e-1, .1388614678, .2328759081, 0.244336214e-1, .1394893808, .2328759200, 0.2443364533e-1, .1394893543]]

[[.1, 0.769540597e-1, .1477783335, .1393069312, 0.763361154e-1, .1477867626, .1393072151, 0.763361266e-1, .1477867830, .1393071934], [.3, .1093424148, .1120401102, .1509302274, .1072278404, .1121142033, .1509369166, .1072278479, .1121142168, .1509369024], [.5, .1392030568, 0.853083077e-1, .1558066181, .1353291378, 0.855066806e-1, .1558355785, .1353291558, 0.8550671332e-1, .1558355439], [.7, .1662374563, 0.652194693e-1, .1562235596, .1604342222, 0.655908735e-1, .1562974878, .1604342352, 0.6559089617e-1, .1562974637], [.9, .1903821623, 0.500537619e-1, .1537887672, .1825594352, 0.506356391e-1, .1539346707, .1825594528, 0.5063567192e-1, .1539346352], [1.1, .2117168860, 0.385555127e-1, .1496220815, .2018541863, 0.393727175e-1, .1498707561, .2018542024, 0.3937274753e-1, .1498707234], [1.3, .2303874000, 0.298096396e-1, .1444864012, .2185409755, 0.308687065e-1, .1448804021, .2185409880, 0.3086872986e-1, .1448803765], [1.5, .2465077820, 0.231661161e-1, .1388614678, .2328759081, 0.244336214e-1, .1394893808, .2328759200, 0.2443364533e-1, .1394893543]]

 (1)
> 

t := [seq(Data[i, 1], i = 1 .. nops(Data))]

[.1, .3, .5, .7, .9, 1.1, 1.3, 1.5]

 (2)
> 

s1 := [seq(Data[i, 2], i = 1 .. nops(Data))]

[0.769540597e-1, .1093424148, .1392030568, .1662374563, .1903821623, .2117168860, .2303874000, .2465077820]

 (3)
> 

s2 := [seq(Data[i, 5], i = 1 .. nops(Data))]

[0.763361154e-1, .1072278404, .1353291378, .1604342222, .1825594352, .2018541863, .2185409755, .2328759081]

 (4)
> 

s3 := [seq(Data[i, 8], i = 1 .. nops(Data))]

[0.763361266e-1, .1072278479, .1353291558, .1604342352, .1825594528, .2018542024, .2185409880, .2328759200]

 (5)
> 

p1 := plot(t, s1, color = red)
> 

p2 := plot(t, s2, color = green)
> 

p3 := plot(t, s3, color = blue)
> 

display(p1, p2, p3, labels = ["t", " Proportions of Susceptible"], labeldirections = [horizontal, vertical], thickness = 4)

 
> 

NULL
> 

NULL
> 

NULL
> 

NULL
> 

NULL


 

Download ADM_RKF45_Comparison2.mw

How to Plot Multiple Graphs for Comparis...

Elisha 35
December 30 2017
0 0

@gkokovidis Thanks alot. I just did this as you advised. Why is the graph not displayed? Pls see below: instead of my plotted graph being displayed, see what was displayed:  display(PLOT(`...`), PLOT(`...`), PLOT(`...`))

The work is shown below.
 

``

> 

restart; with*plots
> 

Data := [[.1, 0.769540597e-1, .1477783335, .1393069312, 0.763361154e-1, .1477867626, .1393072151, 0.763361266e-1, .1477867830, .1393071934], [.3, .1093424148, .1120401102, .1509302274, .1072278404, .1121142033, .1509369166, .1072278479, .1121142168, .1509369024], [.5, .1392030568, 0.853083077e-1, .1558066181, .1353291378, 0.855066806e-1, .1558355785, .1353291558, 0.8550671332e-1, .1558355439], [.7, .1662374563, 0.652194693e-1, .1562235596, .1604342222, 0.655908735e-1, .1562974878, .1604342352, 0.6559089617e-1, .1562974637], [.9, .1903821623, 0.500537619e-1, .1537887672, .1825594352, 0.506356391e-1, .1539346707, .1825594528, 0.5063567192e-1, .1539346352], [1.1, .2117168860, 0.385555127e-1, .1496220815, .2018541863, 0.393727175e-1, .1498707561, .2018542024, 0.3937274753e-1, .1498707234], [1.3, .2303874000, 0.298096396e-1, .1444864012, .2185409755, 0.308687065e-1, .1448804021, .2185409880, 0.3086872986e-1, .1448803765], [1.5, .2465077820, 0.231661161e-1, .1388614678, .2328759081, 0.244336214e-1, .1394893808, .2328759200, 0.2443364533e-1, .1394893543]];

[[.1, 0.769540597e-1, .1477783335, .1393069312, 0.763361154e-1, .1477867626, .1393072151, 0.763361266e-1, .1477867830, .1393071934], [.3, .1093424148, .1120401102, .1509302274, .1072278404, .1121142033, .1509369166, .1072278479, .1121142168, .1509369024], [.5, .1392030568, 0.853083077e-1, .1558066181, .1353291378, 0.855066806e-1, .1558355785, .1353291558, 0.8550671332e-1, .1558355439], [.7, .1662374563, 0.652194693e-1, .1562235596, .1604342222, 0.655908735e-1, .1562974878, .1604342352, 0.6559089617e-1, .1562974637], [.9, .1903821623, 0.500537619e-1, .1537887672, .1825594352, 0.506356391e-1, .1539346707, .1825594528, 0.5063567192e-1, .1539346352], [1.1, .2117168860, 0.385555127e-1, .1496220815, .2018541863, 0.393727175e-1, .1498707561, .2018542024, 0.3937274753e-1, .1498707234], [1.3, .2303874000, 0.298096396e-1, .1444864012, .2185409755, 0.308687065e-1, .1448804021, .2185409880, 0.3086872986e-1, .1448803765], [1.5, .2465077820, 0.231661161e-1, .1388614678, .2328759081, 0.244336214e-1, .1394893808, .2328759200, 0.2443364533e-1, .1394893543]]

 (1)
> 

t := [seq(Data[i, 1], i = 1 .. nops(Data))];

[.1, .3, .5, .7, .9, 1.1, 1.3, 1.5]

 (2)
> 

s1 := [seq(Data[i, 2], i = 1 .. nops(Data))];

[0.769540597e-1, .1093424148, .1392030568, .1662374563, .1903821623, .2117168860, .2303874000, .2465077820]

 (3)
> 

s2 := [seq(Data[i, 5], i = 1 .. nops(Data))];

[0.763361154e-1, .1072278404, .1353291378, .1604342222, .1825594352, .2018541863, .2185409755, .2328759081]

 (4)
> 

s3 := [seq(Data[i, 8], i = 1 .. nops(Data))];

[0.763361266e-1, .1072278479, .1353291558, .1604342352, .1825594528, .2018542024, .2185409880, .2328759200]

 (5)
> 

p1 := plot(t, s1, color = red):
> 

p2 := plot(t, s2, color = blue):
> 

p3 := plot(t, s3, color = green):
> 

display(p1, p2, p3);

display(INTERFACE_PLOT(CURVES(Matrix(8, 2, {(1, 1) = .1, (1, 2) = 0.769540597e-1, (2, 1) = .3, (2, 2) = .1093424148, (3, 1) = .5, (3, 2) = .1392030568, (4, 1) = .7, (4, 2) = .1662374563, (5, 1) = .9, (5, 2) = .1903821623, (6, 1) = 1.1, (6, 2) = .211716886, (7, 1) = 1.3, (7, 2) = .2303874, (8, 1) = 1.5, (8, 2) = .246507782}, datatype = float[8])), COLOUR(RGB, 1.00000000, 0., 0.), AXESLABELS("", ""), VIEW(DEFAULT, DEFAULT)), INTERFACE_PLOT(CURVES(Matrix(8, 2, {(1, 1) = .1, (1, 2) = 0.763361154e-1, (2, 1) = .3, (2, 2) = .1072278404, (3, 1) = .5, (3, 2) = .1353291378, (4, 1) = .7, (4, 2) = .1604342222, (5, 1) = .9, (5, 2) = .1825594352, (6, 1) = 1.1, (6, 2) = .2018541863, (7, 1) = 1.3, (7, 2) = .2185409755, (8, 1) = 1.5, (8, 2) = .2328759081}, datatype = float[8])), COLOUR(RGB, 0., 0., 1.00000000), AXESLABELS("", ""), VIEW(DEFAULT, DEFAULT)), INTERFACE_PLOT(CURVES(Matrix(8, 2, {(1, 1) = .1, (1, 2) = 0.763361266e-1, (2, 1) = .3, (2, 2) = .1072278479, (3, 1) = .5, (3, 2) = .1353291558, (4, 1) = .7, (4, 2) = .1604342352, (5, 1) = .9, (5, 2) = .1825594528, (6, 1) = 1.1, (6, 2) = .2018542024, (7, 1) = 1.3, (7, 2) = .218540988, (8, 1) = 1.5, (8, 2) = .23287592}, datatype = float[8])), COLOUR(RGB, 0., 1.00000000, 0.), AXESLABELS("", ""), VIEW(DEFAULT, DEFAULT)))

 (6)
> 

``
> 

``
> 

``
> 

``
> 

``
> 

``
> 

``

``


 

Download ADM_RKF45_COMPARISON.mw

How to Plot Multiple Graphs for Comparis...

Elisha 35
December 29 2017
0 0

@Elisha 

I tried writing the code as you guided me but see the error i encountered:

Data:=readdata("c:/Users/kokoge00/Desktop/methods.dat",float,10);
Error, (in readline) file or directory does not exist.

Pls guide me on how to write this code to avoid this error.

Thanks

 

How to Plot Multiple Graphs for Comparis...

Elisha 35
December 29 2017
0 0

@gkokovidis Thanks Man. You are a gem!!!

It worked!...

Elisha 35
May 17 2017
0 0

@tomleslie Thanks alot! It really worked.

 

How to get exact solution using Maple...

Elisha 35
May 16 2017
0 1

@Carl Love Pls see what I did but seems am not yet home.How can I get numeric solution for values of t=0.1, 0.3, 0.5, 0.7, 0.9, 1.1, 1.3, 1.5 in this system of ODE?


 

``

> 

odesys := {diff(e(t), t) = lambda*s(t)-(delta+a+epsilon)*e(t), diff(i(t), t) = delta*e(t)-(eta+a+epsilon)*i(t), diff(r(t), t) = eta*i(t)+f*theta[2]*v(t)-(a+epsilon)*r(t), diff(s(t), t) = (1-phi)*epsilon+(1-rho)*a+(1-f)*alpha*v(t)-(lambda+theta[1]+a+epsilon)*s(t), diff(v(t), t) = phi*epsilon+rho*a+theta[1]*s(t)-((1-f)*alpha+f*theta[2]+a+epsilon)*v(t)};

{diff(e(t), t) = lambda*s(t)-(delta+a+epsilon)*e(t), diff(i(t), t) = delta*e(t)-(eta+a+epsilon)*i(t), diff(r(t), t) = eta*i(t)+f*theta[2]*v(t)-(a+epsilon)*r(t), diff(s(t), t) = (1-phi)*epsilon+(1-rho)*a+(1-f)*alpha*v(t)-(lambda+theta[1]+a+epsilon)*s(t), diff(v(t), t) = phi*epsilon+rho*a+theta[1]*s(t)-((1-f)*alpha+f*theta[2]+a+epsilon)*v(t)}

 (1)
> 

v(0) := .4;

.4

 (2)
> 

NULL
> 

s(0) := 0.6e-1;

0.6e-1

 (3)
> 

e[0] := .24;

.24

 (4)
> 

i[0] := .17;

.17

 (5)
> 

r[0] := .13;

.13

 (6)
> 

c := 0.4e-1;

0.4e-1

 (7)
> 

f := .4;

.4

 (8)
> 

beta := .2;

.2

 (9)
> 

epsilon := .8;

.8

 (10)
> 

theta[1] := .1;

.1

 (11)
> 

theta[2] := .3;

.3

 (12)
> 

alpha := .9;

.9

 (13)
> 

rho := .7;

.7

 (14)
> 

eta := .99;

.99

 (15)
> 

delta := .3;

.3

 (16)
> 

a := 0.4e-1;

0.4e-1

 (17)
> 

phi := 1;

1

 (18)
> 

lambda := 0.96e-1;

0.96e-1

 (19)
> 

('`union`')(`~`[indets](odesys)[]);

`union`({t, s(t), v(t), diff(s(t), t)}, {t, s(t), v(t), diff(v(t), t)}, {t, s(t), diff((table( [( 0 ) = .24 ] ))(t), t), (table( [( 0 ) = .24 ] ))(t)}, {t, diff((table( [( 0 ) = .17 ] ))(t), t), (table( [( 0 ) = .17 ] ))(t), (table( [( 0 ) = .24 ] ))(t)}, {t, v(t), diff((table( [( 0 ) = .13 ] ))(t), t), (table( [( 0 ) = .13 ] ))(t), (table( [( 0 ) = .17 ] ))(t)})

 (20)
> 

dsolve(odesys)

Error, (in dsolve) invalid input: D expects its 1st argument, f, to be of type {set, array, list, algebraic, equation, procedure}, but received table( [( 0 ) = .13 ] )

  
> 

``

``


 

Download odesys.mw

1 2 Page 1 of 2