Year: 2015
Author: Xiao-Hui Liu, Yujiang Wu, Jinyun Yuan, Raimundo J. B. de Sampaio, Yan-Tao Wang
Journal of Mathematical Study, Vol. 48 (2015), Iss. 1 : pp. 30–52
Abstract
Based on high-order linear multistep methods (LMMs), we use the class of extended trapezoidal rules (ETRs) to solve boundary value problems of ordinary differential equations (ODEs), whose numerical solutions can be approximated by boundary value methods (BVMs). Then we combine this technique with fourth-order Padé compact approximation to discrete 2D Schrödinger equation. We propose a scheme with sixth-order accuracy in time and fourth-order accuracy in space. It is unconditionally stable due to the favourable property of BVMs and ETRs. Furthermore, with Richardson extrapolation, we can increase the scheme to order 6 accuracy both in time and space. Numerical results are presented to illustrate the accuracy of our scheme.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v48n1.15.03
Journal of Mathematical Study, Vol. 48 (2015), Iss. 1 : pp. 30–52
Published online: 2015-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Schrödinger equation BVMs ETRs compact scheme Richardson extrapolation.