0
$\begingroup$

In physics, there are a lot of cases of ordinary differential equation with complex coefficients. Or there are cases where solution of ODE with real coefficients is complex number.

What is numerical method for such cases? Can we just use methods used for real-coefficient/real-valued ODE?

$\endgroup$
  • 2
    $\begingroup$ Yes, you can. Algebraic operations work the same. $\endgroup$ – user147263 Sep 22 '15 at 20:24
  • $\begingroup$ There exist some schemes, for example Rosenbrock schemes with complex coefficients, that achieve higher order or have some nice properties when complex arithmetics is allowed. $\endgroup$ – uranix Sep 22 '15 at 22:30
0
$\begingroup$

Standard methods for real coefficients will work. In fact, the test method for A-stability usually has solve solving for a timestep to the linear problem with a complex coefficients (simulating complex eigenvalues of the Jacobian). Thus for all of the main methods it's well known what the stability is when you have complex numbers.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.