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Structure-Preserving Wavelet Algorithms for the Nonlinear Dirac Model

Published online by Cambridge University Press:  18 January 2017

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:[email protected] (S. H. Song)
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Abstract

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.

Type
Research Article
Copyright
Copyright © Global-Science Press 2017 

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