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July 21st, 2011, 01:14 AM   #1
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Complex system of ODE

Hello!

I have to solve a system of differential equations like this

where --- complex vector and matrix, respectively; assume that are known.

Let's find a solution . And so, we get the eigenvalue and eigenvector problem with general complex non-symmetric matrix .
I code it using FORTRAN and I use libraries to find the eigenvalues and eigenvectors.
And so, the general solution looks like this

I have some doubt about matrix and about my system of ODE.
First of all. Does it the SODE with constant coefficients ? The matrix depends parametrically from .
Secondly. Are the general solution coefficients different at each ? And Must I find it from several conditions, for example, ?
Finally. Should I solve this SODE with conventional numerical methods, like Runge-Kutta 4th order (I have the initial conditions for vector )?

Thank you very much.
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