How can I solve the following PDE?

$\dotA(t)=rA(t)-\frac{A(t)^2}{4c}+1$

$\dotB(t)=rB(t)-aA(t)$

$A(T)=q,B(T)=0.$

Suppose that r=0.02, a=3, c=1,q=1.5.

How to write a code to solve it.

Answer 1

[Alan Stevens]

Try setting tau = T - t, so that dA/dt = -dA/dtau etc, and A(T) , B(T) become A(0), B(0). i.e. turn the boundary value problem into an initial value problem.

Answer 2

[Torsten]

MATLAB allows you to integrate backwards in time simply by defininig tspan starting with T and ending with 0.

And why do you say it's a PDE ? As far as I can see from your description, it's an ODE.