On Fourier Time-Splitting Methods for Nonlinear Schrödinger Equations in the Semiclassical Limit
On Fourier Time-Splitting Methods for Nonlinear Schrödinger Equations in the Semiclassical Limit
We prove an error estimate for a Lie--Trotter splitting operator associated with the Schrödinger--Poisson equation in the semiclassical regime, when the WKB approximation is valid. In finite time, and so long as the solution to a compressible Euler--Poisson equation is smooth, the error between the numerical solution and the exact …