The numerical solution of the nonlinear Klein-Gordon and Sine-Gordon equations using the Chebyshev tau meshless method

Wenting Shao; Xionghua Wu

doi:10.1016/j.cpc.2014.02.002

The numerical solution of the nonlinear Klein-Gordon and Sine-Gordon equations using the Chebyshev tau meshless method

Wenting Shao
, Xionghua Wu^*

^*Corresponding author for this work

School of Mathematics and Physics

Tongji University

Research output: Contribution to journal › Article › peer-review

27 Citations (Scopus)

Abstract

In this work, we study the numerical solutions of one-dimensional Klein-Gordon and Sine-Gordon equations using the Chebyshev tau meshless method based on the integration-differentiation (CTMMID). First, we apply CTMMID to discretize both space and time variables. The initial and boundary conditions could be incorporated efficiently with full CTMMID. Furthermore, we introduce the Domain Decomposition Method (DDM) in space and the block-marching technique in time for problems defined in large interval and long time computing. The numerical results are more accurate and with less computational effort than some existing studies.

Original language	English
Pages (from-to)	1399-1409
Number of pages	11
Journal	Computer Physics Communications
Volume	185
Issue number	5
DOIs	https://doi.org/10.1016/j.cpc.2014.02.002
Publication status	Published - May 2014

Keywords

Block-marching technique
Chebyshev tau meshless method
Domain Decomposition Method
Integration-differentiation
Klein-Gordon equation
Sine-Gordon equation

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10.1016/j.cpc.2014.02.002

Cite this

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title = "The numerical solution of the nonlinear Klein-Gordon and Sine-Gordon equations using the Chebyshev tau meshless method",

abstract = "In this work, we study the numerical solutions of one-dimensional Klein-Gordon and Sine-Gordon equations using the Chebyshev tau meshless method based on the integration-differentiation (CTMMID). First, we apply CTMMID to discretize both space and time variables. The initial and boundary conditions could be incorporated efficiently with full CTMMID. Furthermore, we introduce the Domain Decomposition Method (DDM) in space and the block-marching technique in time for problems defined in large interval and long time computing. The numerical results are more accurate and with less computational effort than some existing studies.",

keywords = "Block-marching technique, Chebyshev tau meshless method, Domain Decomposition Method, Integration-differentiation, Klein-Gordon equation, Sine-Gordon equation",

author = "Wenting Shao and Xionghua Wu",

note = "Funding Information: The support from the National Natural Science Foundation of China under grants (No. 10671146 and No. 50678122 ) is fully acknowledged. The authors are very grateful to the reviewers for carefully reading the paper and for their comments and suggestions which have improved the paper very much. ",

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doi = "10.1016/j.cpc.2014.02.002",

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T1 - The numerical solution of the nonlinear Klein-Gordon and Sine-Gordon equations using the Chebyshev tau meshless method

AU - Shao, Wenting

AU - Wu, Xionghua

N1 - Funding Information: The support from the National Natural Science Foundation of China under grants (No. 10671146 and No. 50678122 ) is fully acknowledged. The authors are very grateful to the reviewers for carefully reading the paper and for their comments and suggestions which have improved the paper very much.

PY - 2014/5

Y1 - 2014/5

N2 - In this work, we study the numerical solutions of one-dimensional Klein-Gordon and Sine-Gordon equations using the Chebyshev tau meshless method based on the integration-differentiation (CTMMID). First, we apply CTMMID to discretize both space and time variables. The initial and boundary conditions could be incorporated efficiently with full CTMMID. Furthermore, we introduce the Domain Decomposition Method (DDM) in space and the block-marching technique in time for problems defined in large interval and long time computing. The numerical results are more accurate and with less computational effort than some existing studies.

AB - In this work, we study the numerical solutions of one-dimensional Klein-Gordon and Sine-Gordon equations using the Chebyshev tau meshless method based on the integration-differentiation (CTMMID). First, we apply CTMMID to discretize both space and time variables. The initial and boundary conditions could be incorporated efficiently with full CTMMID. Furthermore, we introduce the Domain Decomposition Method (DDM) in space and the block-marching technique in time for problems defined in large interval and long time computing. The numerical results are more accurate and with less computational effort than some existing studies.

KW - Block-marching technique

KW - Chebyshev tau meshless method

KW - Domain Decomposition Method

KW - Integration-differentiation

KW - Klein-Gordon equation

KW - Sine-Gordon equation

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U2 - 10.1016/j.cpc.2014.02.002

DO - 10.1016/j.cpc.2014.02.002

M3 - Article

AN - SCOPUS:84900237421

SN - 0010-4655

VL - 185

SP - 1399

EP - 1409

JO - Computer Physics Communications

JF - Computer Physics Communications

IS - 5

ER -

The numerical solution of the nonlinear Klein-Gordon and Sine-Gordon equations using the Chebyshev tau meshless method

Abstract

Keywords

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