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Zbl 1208.65130
Liao, Hong-Lin; Sun, Zhi-Zhong; Shi, Han-Sheng
Error estimate of fourth-order compact scheme for linear Schrödinger equations. (English)
[J] SIAM J. Numer. Anal. 47, No. 6, 4381-4401 (2010). ISSN 0036-1429; ISSN 1095-7170/e

A fourth-order compact difference scheme is proposed for solving multidimensional linear Schrödinger equations with periodic boundary conditions. Based on a coupled system of the initial-boundary value problem a novel technique of $H^2$ error analysis is introduced to analyze the compact difference method. With an asymptotic expansion of the numerical solution, two higher-order stable approximations are obtained. Theoretical results are supported by numerical tests.
[Pavol Chocholatý (Bratislava)]

MSC 2000:: *65M06 Finite difference methods (IVP of PDE)
65M12 Stability and convergence of numerical methods (IVP of PDE)
65M15 Error bounds (IVP of PDE)

Keywords: linear Schrödinger equation; fourth-order compact scheme; discrete energy analysis; maximum norm error estimate; asymptotic expansion

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