Delali Accolley

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15 years, 9 days

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These are questions asked by Delali Accolley

Hi, I would appreciate some help in solving the following system of partial differential equations. The particularity of the system is that only the individual variables (i.e. a, c, and l) depend on two arguments (t: current time period and v: date of birth). The other variables are either rates or aggregates. The aggregate variables (i.e. K, L, and Y) depend only on time, t, because they are the integrals of the individual variables over v. Thanks for your help.

NULL

NULL

restart; with(PDEtools)

alpha := .3306341; delta := solve(1+0.4877489e-1 = exp(delta_a)); T := 1

l0 := 42.375*(33.16667/(52*(24-9.95)*7)); L0 := l0*T

x0 := 0

IOR := .2093723865

KOR := IOR/delta

r0 := alpha/KOR-delta; rho := r0; fsolve({K0 = Y0*KOR, w0 = (1-alpha)*Y0/L0, alpha*exp(x0)*K0^(alpha-1)*L0^(1-alpha) = r0+delta}); assign(%)

0.2758153402e-1

 

{K0 = 2.510740299, Y0 = .5710794198, w0 = 1.390997088}

(1)

C0 := -K0*delta+Y0; c0 := C0/T

.4515111588

 

.4515111588

(2)

sigma := w0*(1-l0)/c0

2.234133040

(3)

eq1 := diff(c(t, v), t) = (r(t)-rho)*c(t, v)

eq2 := sigma*c(t, v) = w(t)*(1-l(t, v))

eq3 := r(t)*a(t, v)+w(t)*l(t, v) = c(t, v)+diff(a(t, v), t)

eq4 := Y(t) = exp(x(t))*K(t)^alpha*L(t)^(1-alpha)

eq5 := r(t)-delta = alpha*Y(t)/K(t)

eq6 := w(t) = (1-alpha)*Y(t)/L(t)

eq7 := K(t) = int(a(t, v), v = t-T .. t)

eq8 := L(t) = int(l(t, v), v = t-T .. t)

eq9 := x(t) = piecewise(t = 0, 0, t > 0, 0.1e-1)

eq := {eq1, eq2, eq3, eq4, eq5, eq6, eq7, eq8, eq9}

SV := {K(0) = K0, L(0) = L0, Y(0) = Y0, a(t, 0) = 0, c(0, 0) = c0, l(0, 0) = l0, r(0) = r0, w(0) = w0}

pdsolve(eq, SV, numeric, 'time' = t, 'range' = 0 .. T)

Error, (in pdsolve/numeric/process_PDEs) variable(s) {v} are in the PDE system but are not dependent or independent variables

 

sol := pdsolve(eq, SV, 'time' = t, 'range' = 0 .. T)

(4)

NULL

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Hi, I would be grateful if anyone could help find inconsistency in a system of equations I have been solving. I can easily solve the system (that I have called ‘EQs’) when I set the parameter ‘tau\_l’ equal to .06, but for a different value, it will not solve. The same thing happens whenever I change the value of some other parameters like ‘l3’. Regards

ACCOLLEY_Delali_-_Demographics_3.mw

Hi, I'm trying to solve without success numerically the following system of 15 nonlinear equations. Could anyone help, please? Thanks
 

restart

n := 0.27231149e-1:

x := 0.5116034663e-1:

F := .1561816797:

eq1 := sigma*C0 = pgamma*W*H1*(1-E0-L0)/(1+n):

eq2 := sigma*C1 = W*H1*(1-L1):

eq3 := (1+R)*C0 = (1+rho)*exp(x)*C1:

eq4 := (1+R)*C1 = (1+rho)*exp(x)*C2:

eq5 := C1 = (1+phi)*C0:

eq6 := pgamma*L0+pgamma*(1+(1+n)*F/(pgamma*W*H1))*E0+L1 = (1+R)*(1+(1+n)*F/(pgamma*W*H1))/(ppsi*exp(x))-pgamma*(1+(1+n)*F/(pgamma*W*H1))/ppsi:

eq7 := 1 = pgamma*(1+ppsi*E0)/(1+n):

eq8 := exp(x)*A1 = pgamma*W*L0*H1/(1+n)+Epsilon1-C0-F*E0:

eq9 := exp(x)*A2 = W*L1*H1+(1+R)*A1-C1-(1+n)*Epsilon1:

eq10 := (1+R)*A2 = C2:

eq11 := Y = H^alpha*K^(1-alpha):

eq12 := alpha*Y = W*H:

eq13 := (1-alpha)*Y = (1+R)*K:

eq14 := K = A1/(1+n)+A2/(1+n)^2:

eq15 := H = (pgamma*L0+L1)*H1/(1+n):

eq := {eq1, eq2, eq3, eq4, eq5, eq6, eq7, eq8, eq9, eq10, eq11, eq12, eq13, eq14, eq15}:

vars := {A1, A2, C0, C1, C2, E0, H, H1, K, L0, L1, R, W, Y, Epsilon1}:

NULL

fsolve(eq, vars); 1; assign(%)

fsolve({1 = .6865382886+.1072247031*E0, C1 = 1.475639047*C0, H = .9734907289*(.7052335150*L0+L1)*H1, K = .9734907289*A1+.9476841993*A2, Y = H^.6874443*K^.3125557, (1+R)*A2 = C2, (1+R)*C0 = 1.121850394*C1, (1+R)*C1 = 1.121850394*C2, 1.052491643*A1 = .6865382886*W*L0*H1+Epsilon1-C0-.1561816797*E0, 1.052491643*A2 = W*L1*H1+(1+R)*A1-C1-1.027231149*Epsilon1, 5.171201776*C0 = .6865382886*W*H1*(1-E0-L0), 5.171201776*C1 = W*H1*(1-L1), .3125557*Y = (1+R)*K, .6874443*Y = W*H, .7052335150*L0+.7052335150*(1+.2274915796/(W*H1))*E0+L1 = 6.083468374*(1+R)*(1+.2274915796/(W*H1))-4.515468884-1.027231149/(W*H1)}, {A1, A2, C0, C1, C2, E0, H, H1, K, L0, L1, R, W, Y, Epsilon1})

(1)

``

 

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