High-order implicit Galerkin-Legendre spectral method for the two-dimensional Schrodinger equation
Numerical Analysis
2018-11-12 v2
Abstract
In this paper, we propose Galerkin-Legendre spectral method with implicit Runge-Kutta method for solving the unsteady two-dimensional Schrodinger equation with nonhomogeneous Dirichlet boundary conditions and initial condition. We apply a Galerkin-Legendre spectral method for discretizing spatial derivatives, and then employ the implicit Runge-Kutta method for the time integration of the resulting linear first-order system of ordinary differential equations in complex domain. We derive the spectral rate of convergence for the proposed method in the L^2-norm for the semidiscrete formulation. Numerical experiments show our formulation have high-order accurate, and have the exponential rates of convergence in space.
Cite
@article{arxiv.1607.08420,
title = {High-order implicit Galerkin-Legendre spectral method for the two-dimensional Schrodinger equation},
author = {Wenjie Liu and Boying Wu},
journal= {arXiv preprint arXiv:1607.08420},
year = {2018}
}