How to Solve ODEs with Complex Coefficients Numerically?

[Massimo33]

Hello,

I have a nonlinear ODE with complex coefficients and need to solve it numerically. In general, I even understand what method I am going to use but how to develop the method for such kind of equations. Many packages (e.g. IMSL) or solver have routines to deal with the complex variables but I am not sure about the routines for ODE solving. So my question is, first, is it possible to apply IMSL ODE routines in that case keeping in mind, my coefficients are not elementary or transcendental functions but user defined one (some array, actually)? And second, how to implement such kind of things "by hands", e.g. If I need to implement Runge-Kutta method for an equation with complex coefficients, how to do it because I know the algorithm, I understand how to do it for real variables and coefficients but the complex case seems to be difficult. And any advice or recommendations about using some other (accessible) solvers or packages for this problem.

I would greatly appreciate any advice or help

 

[HallsofIvy]

I can see no reason why you would need to change "Runge-Kutta" at all. The algorithm does not assume real coefficients. As long as you are careful to use complex number arithmetic, the algorithm should work just as well with complex numbers as with real numbers.