Low Regularity Exponential-Type Integrators for Semilinear Schrödinger Equations
Low Regularity Exponential-Type Integrators for Semilinear Schrödinger Equations
We introduce low regularity exponential-type integrators for nonlinear Schrödinger equations for which first-order convergence only requires the boundedness of one additional derivative of the solution. More precisely, we will prove first-order convergence in $$H^r$$ for solutions in $$H^{r+1}$$ (with $$r > d/2$$ ) of the derived schemes. This allows us …