Hi there,

Is there a way in which i can solve the following optimal control problem numerically with Maple?

 dH/dt=λ-µ H-(1-u1)β H V+δ I,

dI/dt=(1-u1)β H V-σ I,

‎dV/dt=(1-u2)k I-γ‎V,

dλ1/dt=-1+λ1µ+β‎‎V(1-u1)(λ1-λ2),‎

dλ2/dt=λ1δ+λ2σ-λ3(1-u2)k‎,‎

‎dλ3/dt=β H(λ1-λ2)(1-u1)‎‎+λ3γ.

where

u1=βHV(λ1-λ2)/A1,

u2=-λ3kI/A2,

σ = α + δ,

and

H(0)=1.7*10^8,    I(0)=0,    V(0)=400.

λ=5*10^5,    µ=0.003,     β=4*10^(-10),    α=0.043,    δ= 0.2                  k=6.24,       γ‎=0.65.

A1=900, A2=1000.

Answers and advice are very appreciated. 

Thank you all for reading.

Aylin

Hi all,

I try  to plot phase portrait the below DAEs, 

diff(S(t), t)=-β*(1+δ*sin2Πt)*S(t)*I(t)-μ*S(t)+μ,

diff(I(t), t)=β*(1+δ*sin2Πt)*S(t)*I(t)-γ*I(t)-μ*I(t),

0=S(t)+I(t)+R(t)-1.

where

μ=0.01,

β=1510,

δ=0.02,

γ=50,

I really appreciate your help.

Hi,

Dear Experts,

When I run this code in maple I am facing with "Error, (in dsolve/numeric/bvp) initial Newton iteration is not converging".

restart:
 
 unprotect('gamma');
 lambda:=5*10^5:
 mu:=0.003:
 beta:=4*10^(-10):
 delta:=0.2:
 alpha:=0.043:
 sigma:=alpha+delta:
 k:=6.24:
 gamma:=0.65:
 A[1]:=1:
 A[2]:=1:

ics := x[1](0)=1.7*10^8, x[2](0)=0,x[3](0)=400,psi[1](50)=0,psi[2](50)=0,psi[3](50)=0:

ode1:=diff(x[1](t), t)=lambda-mu*x[1](t)-(1-beta*x[1](t)*x[3](t)*(psi[1](t)-psi[2](t))/A[1])*beta*x[1](t)*x[3](t)+delta*x[2](t),
 diff(x[2](t), t) =(1-beta*x[1](t)*x[3](t)*(psi[1](t)-psi[2](t))/A[1])*beta*x[1](t)*x[3](t)-sigma*x[2](t),
 diff(x[3](t), t) =(1+psi[3](t)*k*x[2](t)/A[2])*k*x[2](t)-gamma*x[3](t),
 diff(psi[1](t), t) =-1+1/A[1]*beta^2*x[1](t)*x[3](t)^2*(psi[1](t)-psi[2](t))^2-psi[1](t)*(-mu+beta^2*x[3](t)^2*(psi[1](t)-psi[2](t))/A[1]*x[1](t)-(1-beta*x[1](t)*x[3](t)*(psi[1](t)-psi[2](t))/A[1])*beta*x[3](t))-psi[2](t)*(-beta^2*x[3](t)^2*(psi[1](t)-psi[2](t))/A[1]*x[1](t)+(1-beta*x[1](t)*x[3](t)*(psi[1](t)-psi[2](t))/A[1])*beta*x[3](t)),
> diff(psi[2](t), t) =1/A[2]*psi[3](t)^2*k^2*x[2](t)-psi[1](t)*delta+psi[2](t)*sigma-psi[3](t)*(psi[3](t)*k^2/A[2]*x[2](t)+(1+psi[3](t)*k*x[2](t)/A[2])*k),
> diff(psi[3](t), t) = 1/A[1]*beta^2*x[1](t)^2*x[3](t)*(psi[1](t)-psi[2](t))^2-psi[1](t)*(beta^2*x[1](t)^2*(psi[1](t)-psi[2](t))/A[1]*x[3](t)-(1-beta*x[1](t)*x[3](t)*(psi[1](t)-psi[2](t))/A[1])*beta*x[1](t))-psi[2](t)*(-beta^2*x[1](t)^2*(psi[1](t)-psi[2](t))/A[1]*x[3](t)+(1-beta*x[1](t)*x[3](t)*(psi[1](t)-psi[2](t))/A[1])*beta*x[1](t))+psi[3](t)*gamma;

sol:=dsolve([ode1,ics],numeric, method = bvp[midrich]);

Error, (in dsolve/numeric/bvp) initial Newton iteration is not converging

Please help me to solve this equation on Maple.