Hi Hugo,
From what I understand, you are trying to solve a system of equations whose solution vector contains contra propagating and copropagating vectors with respect to a length parameter(z). It addresses both problems, boundary value problem and an initial condition problem. This is because the components of the solution vector propagate in opposite and same directions simultaneously.
For such problems, one can use solvers specifically designed for boundary value problems, such as “bvp4c” or “bvp5c” in MATLAB. These solvers allow you to specify boundary conditions at both ends of the domain, making them suitable for handling components that propagate in different directions.
For more information on Boundary Value Problems, refer to below MATLAB documentation:
Hope this helps!
