I want to solve a non linear system of equations of a particular kind. I find it hard to formulate clearly so I directly give a simple example.$f''=A(f,g)\\g''=B(f,g)$with the boundary conditions as follow:$f'(0)=g'(0)=0$$f'(\infty)=g'(\infty)=0$At $x=1$, f is continuous but there is a discontinuity for $g$:$f'(1^-)=f'(1^+), ~~~ f(1^-)=f(1^+) \\g(1^-)=g_{left}, ~~~g(1^+)=g_{right} \\$So we can see this as two problems, one for $x<1$, and one for $x>1$, but the boundaries conditions are coupled in $x=1$.When I have an analytical solution, there is no big deal. Solve the problem for each side, then match the solution at $x=1$.I'm not used with numerical methods and I don't even find how to call this problem. I have some ideas to tackle this but I wish to read a bit about that before.
Numerical methods for boundary-value ODEs with a jump condition
ode;nonlinear equations