Only the explicit Euler method successfully solves my ODE

[ChrisRackauckas]

@ash

Why does nothing work but Euler()

Did you change the tolerance? Or Tsit5 with adaptive=false? Most likely what’s happening is just adaptive time stepping is giving you the tolerance you requested, which is not what you were looking for.

@antoine-levitt

Doesn’t answer your original question but this is a time dependent schrodinger equation, right? Have you tried doing explicit time propagation at fixed Hamiltonian (aka exponential splitting). Ie un+1 = exp(-iH(tn)dt) un, all implemented by hand with staticarrays? @ChrisRackauckas will know but I suspect you can’t really do better (does timestep control work for this kind of equation?) I’m very interested in the optimal method to solve this in any case.

For time-dependent Schrodinger, Magnus methods are the method people usually point to.

https://diffeq.sciml.ai/stable/solvers/nonautonomous_linear_ode/#State-Independent-Solvers

Those will use the matrix exponential but mix it with an RK scheme that is optimized by ignoring terms related to state-dependent RHS.

@jagot

When you have really different time scales going on in your system, you may be forced to be very clever in dealing with those: Solving Schrödinger equation in semiclassical regime with highly oscillatory time-dependent potentials - ScienceDirect

Notice this paper uses a Magnus method. So I guess we’re very clever.