Error analysis of a Fourier–Galerkin method applied to the Schrödinger equation

Abstract

We study error and convergence of a fully discrete Fourier–Galerkin scheme to approximate the solutions of the time-dependent cubic Schrödinger equation. The evolution is carried out combining a second-order accurate scheme and a Fourier-spectral discretization in space. The illustrative cases include simulations with analytic periodic standing waves of the Schrödinger equation. The numerical results are in perfect agreement with our analytical results.

Keywords:

• Galerkin method
• Schrödinger equation
• standing waves

AMS Subject Classifications:

• 76B15
• 35R60
• 35Q53

Notes

This work was supported by Universidad del Valle, A. A. 25360, Cali Colombia and Colciencias.