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

被引：3

作者：

Liu, Wenjie ^{[1
]}

Wu, Boying ^{[1
]}

机构：

[1] Harbin Inst Technol, Dept Math, Harbin 150001, Heilongjiang, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2018年 / 324卷

基金：

中国博士后科学基金;

关键词：

Two-dimensional Schrodinger equation; Galerkin-Legendre spectral method; Implicit Runge-Kutta metho; Error estimate; COLLOCATION; SCHEMES;

D O I：

10.1016/j.amc.2017.12.009

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 RungeKutta 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 accuracy. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：59 / 68

页数：10

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