I am seeking to solve a first-order complex matrix differential equation of the form dy/dt=c.H.y, where H is a complex matrix with complex elements, and c is a complex number. Python and cpp offer built-in libraries like 'odeint', 'solve ivp', and 'boost odeint' that can tackle this problem with ease. However, I am facing a challenge finding a suitable package in Fortran that can handle complex numbers and solve this type of ODE effectively. I have explored options such as 'odepack', but it can't handle complex numbers.
Your assistance will be much appreciated.
Hello Debamalya Dutta,
you can try using the slatec library (https://www.netlib.org/slatec/). It might allow you to solve the complex ode.
Sincerely
Pavlo
Or you can represent an n-dimensional complex ODE as a 2n-dimensional real ODE. You could write short adapters that convert to and from n-dim complex vectors and 2n-dim real vectors.
I highly recommend the subroutine 'zvode.f' (https://www.netlib.org/ode/zvode.f).
You should be very careful not to run into numerical issues (numerical roundoff and catastrophic cancellation) when the matrix exponential problem is very stiff. I am not sure about how well these ODE solvers handle such situations, maybe they do. You can also take a look into the famous paper by Moler and Loan, "Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later", just for awareness.
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