Use rk4 (ode45) to get a solution on signals both contra and co propagating

Hi,

I am trying to solve a system of equation where my solution vector looks like among which is contra propagating with respect to a length parameter and is copropagating . I see no issue when defining my parameters (initial condition and solving domain) if all the components of my vectors are going in the same direction, however how do I define them if it is not the case. Is there a known solution when it comes to defining this kind of systems?

I do not need a code just to be pointed to the right direction, please.

(I have been using ode45 for the copropagating case)

Thanks!

Answer 1

[Hitesh]

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:

https://www.mathworks.com/help/matlab/boundary-value-problems.html

Hope this helps!

[Hugo]

Thanks, that is what I was looking for, the method I was using was very slow in comparison (a shooting method where I had to solve my system multiple time until I get the right initial conditions)