Journal
JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS
Volume 10, Issue 6, Pages 2998-3012Publisher
INT SCIENTIFIC RESEARCH PUBLICATIONS
DOI: 10.22436/jnsa.010.06.14
Keywords
2D sine-Gordon equation; conservative; difference scheme; linear iteration; convergence
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Funding
- Science and Technology Department of Sichuan Province in China [2017GZ0316]
- funds of Sichuan Center for Education Development Research of Education Department [CJF15014]
- National Natural Science Funds of China [71471123]
- Fundamental Research Funds for the Central Universities of China [skqy201621]
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We present an efficient second-order finite difference scheme for solving the 2D sine-Gordon equation, which can inherit the discrete energy conservation for the undamped model theoretically. Due to the semi-implicit treatment for the nonlinear term, it leads to a sequence of nonlinear coupled equations. We use a linear iteration algorithm, which can solve them efficiently, and the contraction mapping property is also proven. Based on truncation errors of the numerical scheme, the convergence analysis in the discrete l(2)- norm is investigated in detail. Moreover, we carry out various numerical simulations, such as verifications of the second order accuracy, tests of energy conservation and circular ring solitons, to demonstrate the efficiency and the robustness of the proposed scheme. (C) 2017 All rights reserved.
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