Tamour_Zubair

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These are questions asked by Tamour_Zubair

Hello;

Hope you are fine. I need to learn how can I call my code in the other file of maple, define new value for A and can get results. For this purpose, I just take an simple example as

questionmaple.mw

restart; A := 5; B := 10; AAA[0] := 10; for i from 0 while i <= A do AAA[i+1] := B*i*AAA[0] end do

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(1)
 

``

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Hello Everyone;

Hope you are fine. I need to solve the system of equation. I am using fsolve command but it is not working. Kindly guide me.

Thanks

ques.mw

restart

``

``

Eq[0, 0] := 1.33120000000000000000000000000*lambda[0, 1]+1.33120000000000000000000000000*lambda[0, 2]+1.33120000000000000000000000000*lambda[0, 3]+1.33120000000000000000000000000*lambda[0, 4] = .916487142969312002551492271668:

Eq[0, 1] := 1.32901933598375616624661615670*lambda[0, 1]+1.32901933598375616624661615670*lambda[0, 2]+1.32901933598375616624661615670*lambda[0, 3]+1.32901933598375616624661615670*lambda[0, 4] = 1.09232395220587507357427365904:

Eq[0, 2] := 1.37120000000000000000000000000*lambda[0, 1]+1.37120000000000000000000000000*lambda[0, 2]+1.37120000000000000000000000000*lambda[0, 3]+1.37120000000000000000000000000*lambda[0, 4] = 1.25415129307905065856083635281:

Eq[0, 3] := .966980664016243833753383843299*lambda[0, 1]+.966980664016243833753383843299*lambda[0, 2]+.966980664016243833753383843299*lambda[0, 3]+.966980664016243833753383843299*lambda[0, 4] = 1.37114174964252179339832329224:

``

``

fsolve({seq(Eq[0, ii1], ii1 = 0 .. 3)});

fsolve({.966980664016243833753383843299*lambda[0, 1]+.966980664016243833753383843299*lambda[0, 2]+.966980664016243833753383843299*lambda[0, 3]+.966980664016243833753383843299*lambda[0, 4] = 1.37114174964252179339832329224, 1.32901933598375616624661615670*lambda[0, 1]+1.32901933598375616624661615670*lambda[0, 2]+1.32901933598375616624661615670*lambda[0, 3]+1.32901933598375616624661615670*lambda[0, 4] = 1.09232395220587507357427365904, 1.33120000000000000000000000000*lambda[0, 1]+1.33120000000000000000000000000*lambda[0, 2]+1.33120000000000000000000000000*lambda[0, 3]+1.33120000000000000000000000000*lambda[0, 4] = .916487142969312002551492271668, 1.37120000000000000000000000000*lambda[0, 1]+1.37120000000000000000000000000*lambda[0, 2]+1.37120000000000000000000000000*lambda[0, 3]+1.37120000000000000000000000000*lambda[0, 4] = 1.25415129307905065856083635281}, {lambda[0, 1], lambda[0, 2], lambda[0, 3], lambda[0, 4]})

(1)

``

``

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Hello Everyone;

Hope you are fine. My problem is convert into nonlinear system of ODE's and further i need make the code of apply rk-4 for the formulated ODE's. Kindly guide me. The file is attached. I am waiting for your kind response.

Thanks

Question3.mw

 


 

restart

``

var111 := [C[1, 1](t), C[1, 2](t), C[1, 3](t), C[2, 1](t), C[2, 2](t), C[2, 3](t), C[3, 1](t), C[3, 2](t), C[3, 3](t), ZETA[1](t), ZETA[2](t), ZETA[3](t)]:

sysM := [diff(C[1, 1](t), t) = -(3/16)*Pi*(C[2, 1](t)+4*C[1, 1](t)), diff(C[1, 2](t), t) = -5*Pi*(C[2, 2](t)+4*C[1, 2](t)), diff(C[1, 3](t), t) = -(945/4)*Pi*(C[2, 3](t)+4*C[1, 3](t)), diff(C[2, 1](t), t) = -(1/8)*Pi*(C[3, 1](t)+6*C[2, 1](t)+6*C[1, 1](t)), diff(C[2, 2](t), t) = -10.4719755119659774615421446110*C[3, 2](t)-62.8318530717958647692528676658*C[2, 2](t)-62.8318530717958647692528676658*C[1, 2](t)-2.38361014507273884349657421134*10^15*ZETA[1](t)*C[1, 1](t), diff(C[2, 3](t), t) = -494.800842940392435057866332869*C[3, 3](t)-2968.80505764235461034719799721*C[2, 3](t)-2968.80505764235461034719799721*C[1, 3](t)-1.35954060126371030332767566128*10^16*ZETA[1](t)*C[1, 2](t)-1.35954060126371030332767566128*10^16*ZETA[2](t)*C[1, 1](t), diff(C[3, 1](t), t) = -(3/8)*Pi*(2*C[3, 1](t)+3*C[2, 1](t)), diff(C[3, 2](t), t) = -62.8318530717958647692528676658*C[3, 2](t)-94.2477796076937971538793014986*C[2, 2](t)-1.12625579354686910355213131486*10^17*ZETA[1](t)*C[2, 1](t), diff(C[3, 3](t), t) = -2968.80505764235461034719799721*C[3, 3](t)-4453.20758646353191552079699581*C[2, 3](t)-6.42382934097103118322326749959*10^17*ZETA[1](t)*C[2, 2](t)-6.42382934097103118322326749959*10^17*ZETA[2](t)*C[2, 1](t), diff(ZETA[1](t), t) = -(1/3)*C[2, 1](t), diff(ZETA[2](t), t) = -(1/3)*C[2, 2](t), diff(ZETA[3](t), t) = -(1/3)*C[2, 3](t)]:

ICS := [C[1, 1] = 0.998238989835086492681507032141e-1, C[1, 2] = -0.137051161872492529218951625903e-1, C[1, 3] = -0.629146365720807620696267926206e-2, C[2, 1] = 0.923300332435106257640735267282e-1, C[2, 2] = -0.126762613568515069966837491839e-1, C[2, 3] = -0.581915808273854734025727975244e-2, C[3, 1] = -0.190143920352772604950256237747e-1, C[3, 2] = 0.261054171122321128306306984717e-2, C[3, 3] = 0.119839394846335068333097530793e-2, ZETA[1] = .464598743230343884242076682299, ZETA[2] = .429720916976380440572769663279, ZETA[3] = -0.884964696113332752036741498040e-1]:

``


 

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Hello Everyone;

Hope you are fine. I have set of following ODE's;

Every variable has two ODE's. I need to take one ODE for each variable. Is that any way?
I am waiting for your kind response.

Thanks

Question2.mw

Hello Everyone;Hope you are fine. I am trying to convert the nonlinear system of ODE's into matric form using the following comand but not working it.

 

Kindly help me to do this. The cose is pasted and also attached. I am waiting for your kind response.

Thanks.

Question1_NEW.mw


 

restart; with(PDEtools, Solve); with(LinearAlgebra); with(plots); with(plottools); printlevel := 2

NULL

ZETA[0] := proc (t) options operator, arrow; 0 end proc:

sys222 := [(3/16)*Pi*C[2, 1](t)+(3/4)*Pi*C[1, 1](t)+diff(C[1, 1](t), t) = 0, 5*Pi*C[2, 2](t)+20*Pi*C[1, 2](t)+diff(C[1, 2](t), t) = 0, 800*ZETA[0](t)*C[1, 1](t)*Pi+(3/4)*Pi*C[2, 1](t)+(3/4)*Pi*C[1, 1](t)+diff(C[2, 1](t), t) = 0, 4320*ZETA[1](t)*C[1, 1](t)*Pi+4320*ZETA[0](t)*C[1, 2](t)*Pi+20*Pi*C[2, 2](t)+20*Pi*C[1, 2](t)+diff(C[2, 2](t), t) = 0, diff(ZETA[1](t), t)+(1/3)*C[2, 1](t) = 0, diff(ZETA[2](t), t)+(1/3)*C[2, 2](t) = 0]

[(3/16)*Pi*C[2, 1](t)+(3/4)*Pi*C[1, 1](t)+diff(C[1, 1](t), t) = 0, 5*Pi*C[2, 2](t)+20*Pi*C[1, 2](t)+diff(C[1, 2](t), t) = 0, (3/4)*Pi*C[2, 1](t)+(3/4)*Pi*C[1, 1](t)+diff(C[2, 1](t), t) = 0, 4320*ZETA[1](t)*C[1, 1](t)*Pi+20*Pi*C[2, 2](t)+20*Pi*C[1, 2](t)+diff(C[2, 2](t), t) = 0, diff(ZETA[1](t), t)+(1/3)*C[2, 1](t) = 0, diff(ZETA[2](t), t)+(1/3)*C[2, 2](t) = 0]

(1)

var1 := {C[1, 1](t), C[1, 2](t), C[2, 1](t), C[2, 2](t), ZETA[1](t), ZETA[2](t)};

{C[1, 1](t), C[1, 2](t), C[2, 1](t), C[2, 2](t), ZETA[1](t), ZETA[2](t)}

(2)

f, diffs := eval(GenerateMatrix(`~`[`-`](`~`[rhs](sys222), `~`[lhs](sys222)), var1))

f, diffs := Matrix(6, 6, {(1, 1) = -(3/4)*Pi, (1, 2) = 0, (1, 3) = -(3/16)*Pi, (1, 4) = 0, (1, 5) = 0, (1, 6) = 0, (2, 1) = 0, (2, 2) = -20*Pi, (2, 3) = 0, (2, 4) = -5*Pi, (2, 5) = 0, (2, 6) = 0, (3, 1) = -(3/4)*Pi, (3, 2) = 0, (3, 3) = -(3/4)*Pi, (3, 4) = 0, (3, 5) = 0, (3, 6) = 0, (4, 1) = 0, (4, 2) = -20*Pi, (4, 3) = 0, (4, 4) = -20*Pi, (4, 5) = 0, (4, 6) = 0, (5, 1) = 0, (5, 2) = 0, (5, 3) = -1/3, (5, 4) = 0, (5, 5) = 0, (5, 6) = 0, (6, 1) = 0, (6, 2) = 0, (6, 3) = 0, (6, 4) = -1/3, (6, 5) = 0, (6, 6) = 0}), Vector(6, {(1) = diff(C[1, 1](t), t), (2) = diff(C[1, 2](t), t), (3) = diff(C[2, 1](t), t), (4) = 4320*ZETA[1](t)*C[1, 1](t)*Pi+diff(C[2, 2](t), t), (5) = diff(ZETA[1](t), t), (6) = diff(ZETA[2](t), t)})

(3)

NULL


 

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