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Structure-Preserving Wavelet Algorithms for the Nonlinear Dirac Model

Part of: Equations of mathematical physics and other areas of application Numerical approximation and computational geometry

Published online by Cambridge University Press:  18 January 2017

Xu Qian ,
Hao Fu  and
Songhe Song
Xu Qian
Affiliation:
Department of Mathematics and Systems Science, National University of Defense Technology, Changsha, Hunan 410072, China Academy of Ocean Science and Engineering, National University of Defense Technology, Changsha, Hunan 410073, China
Hao Fu
Affiliation:
Department of Mathematics and Systems Science, National University of Defense Technology, Changsha, Hunan 410072, China
Songhe Song*
Affiliation:
Department of Mathematics and Systems Science, National University of Defense Technology, Changsha, Hunan 410072, China State Key Laboratory of High Performance Computing, National University of Defense Technology, Changsha, Hunan 410073, China
*
*Corresponding author. Email:shsong@nudt.edu.cn (S. H. Song)

Abstract

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The nonlinear Dirac equation is an important model in quantum physics with a set of conservation laws and a multi-symplectic formulation. In this paper, we propose energy-preserving and multi-symplectic wavelet algorithms for this model. Meanwhile, we evidently improve the efficiency of these algorithms in computations via splitting technique and explicit strategy. Numerical experiments are conducted during long-term simulations to show the excellent performances of the proposed algorithms and verify our theoretical analysis.

Keywords

Structure-preservingwavelet collocationconservation lawsnonlinear Dirac equation

MSC classification

Secondary: 35Q41: Time-dependent Schrödinger equations, Dirac equations 65D30: Numerical integration

Information

Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 9 , Issue 4 , August 2017 , pp. 964 - 989
Copyright
Copyright © Global-Science Press 2017 

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