High-order implicit Galerkin–Legendre spectral method for the two-dimensional Schrödinger equation

Wenjie Liu and Boying Wu

Applied Mathematics and Computation, 2018, vol. 324, issue C, 59-68

Abstract: In this paper, we propose Galerkin–Legendre spectral method with implicit Runge-Kutta method for solving the unsteady two-dimensional Schrödinger 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 L2-norm for the semidiscrete formulation. Numerical experiments show our formulation have high-order accuracy.

Keywords: Two-dimensional Schrödinger equation; Galerkin–Legendre spectral method; Implicit Runge–Kutta metho; Error estimate (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:324:y:2018:i:c:p:59-68

DOI: 10.1016/j.amc.2017.12.009

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