Volume 48, Issue 1
Sixth-order Compact Extended Trapezoidal Rules for 2D Schrödinger Equation

Xiao-Hui Wu ,  Yu-Jiang Wu ,  Jin-Yun Yuan ,  Raimundo J. B. de Sampaio and Yan-Tao Wang

10.4208/jms.v48n1.15.03

J. Math. Study, 48 (2015), pp. 30-52.

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  • 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.

  • History

Published online: 2015-03

  • AMS Subject Headings

65M06, 65M12, 65M15

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