> b) seems more reliable but indeed it seems to only solve equations with > real coefficients. > Usually reinterpreting the NxN complex coefficient matrix and the N-sized solution vector as 2N (x 2N) sized real matrices/vectors does the trick. The ODE procedures don't care if it's real or complex at the lower level, when they look at the abs or tol error they check the absolute difference in the numbers, which comes out right when a complex number is interpreted as a pair of reals.
In Fortran I usually passed those complex matrices as real (basically a passing of pointers), just specifying twice the dimensions, I don't know how easy it is to do in a Julia based solver though...
