Optimized integrating factor technique for Schrödinger-like equations

The integrating factor technique is widely used to solve numerically (in particular) the Schrödinger equation in context of spectral methods. Here, we present an improvement this method exploiting freedom provided by gauge condition potential. Optimal conditions are derived considering and temporal numerical resolution with adaptive embedded scheme arbitrary order. We illustrate approach nonlinear (NLS) Schrödinger–Newton (SN) equations. show that optimization increases significantly overall computational speed, sometimes a five or more. This gain crucial for long time simulations, as, larger steps, less computations performed accumulation round-off errors reduced.