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Delali Accolley

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15 years, 198 days
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These are questions asked by Delali Accolley

Variables with different number of argum...

Delali Accolley 20 Maple 2022
pde differential-equations incomplete-question
February 04 2023
1 5

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
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NULL
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restart; with(PDEtools)
> 

alpha := .3306341; delta := solve(1+0.4877489e-1 = exp(delta_a)); T := 1
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l0 := 42.375*(33.16667/(52*(24-9.95)*7)); L0 := l0*T
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x0 := 0
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IOR := .2093723865
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KOR := IOR/delta
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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)
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C0 := -K0*delta+Y0; c0 := C0/T

.4515111588

  

.4515111588

 (2)
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sigma := w0*(1-l0)/c0

2.234133040

 (3)
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eq1 := diff(c(t, v), t) = (r(t)-rho)*c(t, v)
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eq2 := sigma*c(t, v) = w(t)*(1-l(t, v))
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eq3 := r(t)*a(t, v)+w(t)*l(t, v) = c(t, v)+diff(a(t, v), t)
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eq4 := Y(t) = exp(x(t))*K(t)^alpha*L(t)^(1-alpha)
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eq5 := r(t)-delta = alpha*Y(t)/K(t)
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eq6 := w(t) = (1-alpha)*Y(t)/L(t)
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eq7 := K(t) = int(a(t, v), v = t-T .. t)
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eq8 := L(t) = int(l(t, v), v = t-T .. t)
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eq9 := x(t) = piecewise(t = 0, 0, t > 0, 0.1e-1)
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eq := {eq1, eq2, eq3, eq4, eq5, eq6, eq7, eq8, eq9}
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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}
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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

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

(4)
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NULL

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Problem solving nonlinear equations...

Delali Accolley 20 Maple 13
optimization rootfinding fsolve
January 26 2022
2 8

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

Solving numerically a system of non-line...

Delali Accolley 20
solve fsolve
August 31 2015
2 7

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

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restart
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n := 0.27231149e-1:
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x := 0.5116034663e-1:
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F := .1561816797:
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eq1 := sigma*C0 = pgamma*W*H1*(1-E0-L0)/(1+n):
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eq2 := sigma*C1 = W*H1*(1-L1):
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eq3 := (1+R)*C0 = (1+rho)*exp(x)*C1:
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eq4 := (1+R)*C1 = (1+rho)*exp(x)*C2:
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eq5 := C1 = (1+phi)*C0:
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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:
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eq7 := 1 = pgamma*(1+ppsi*E0)/(1+n):
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eq8 := exp(x)*A1 = pgamma*W*L0*H1/(1+n)+Epsilon1-C0-F*E0:
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eq9 := exp(x)*A2 = W*L1*H1+(1+R)*A1-C1-(1+n)*Epsilon1:
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eq10 := (1+R)*A2 = C2:
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eq11 := Y = H^alpha*K^(1-alpha):
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eq12 := alpha*Y = W*H:
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eq13 := (1-alpha)*Y = (1+R)*K:
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eq14 := K = A1/(1+n)+A2/(1+n)^2:
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eq15 := H = (pgamma*L0+L1)*H1/(1+n):
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eq := {eq1, eq2, eq3, eq4, eq5, eq6, eq7, eq8, eq9, eq10, eq11, eq12, eq13, eq14, eq15}:
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vars := {A1, A2, C0, C1, C2, E0, H, H1, K, L0, L1, R, W, Y, Epsilon1}:
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NULL
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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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``

 

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