Given non-commuting matrices and of order , is there a closed-form solution to the differential equation
I know that for the reals, is the general solution to , but I'm also 99% certain this relies on the commutivity of the reals.
I'm more specifically looking to numerically compute given the more general differential equation
but in circumstances where may be large and a 1st order piecewise approximation would be far more accurate than 0th order for any given . Ultimately my concern is computing as quickly as possible.
Are there better techniques for accomplishing this?