As a variation on my previous post I have two ordinary differential equations:
$\quad$ $\frac{dP}{dx}$ = $f(x,P,T)$
$\quad$ $\frac{dT}{dx}$ = $g(x,P,T)$
which I need to integrate from $x$ = $0$ to $x=X$.
The boundary condition on $P$ is at $x=0$, however the boundary condition on $T$ is at $x=X$. So $P=P_0$ at $x=0$ and $T=T_f$ at $x=X$.
What is the best ODE method to use to tackle this problem?
(I am currently using Runge-Kutta with automated step length control for the situation where the boundary condition on $T$ is also at $x=0$, which works fine as I just move in steps from $x$ = $0$ to $x=X$ but cannot do that here as I do not have $T_0$ at $x=0$)