A conservative difference scheme for the Riesz space-fractional sine-Gordon equation
Abstract In this paper, we study a conservative difference scheme for the sine-Gordon equation (SGE) with the Riesz space fractional derivative. We rigorously establish the conservation property and solvability of the difference scheme. We discuss the stability and convergence of the difference sche...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-07-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-018-1689-5 |
| _version_ | 1828965358846869504 |
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| author | Zhiyong Xing Liping Wen |
| author_facet | Zhiyong Xing Liping Wen |
| author_sort | Zhiyong Xing |
| collection | DOAJ |
| description | Abstract In this paper, we study a conservative difference scheme for the sine-Gordon equation (SGE) with the Riesz space fractional derivative. We rigorously establish the conservation property and solvability of the difference scheme. We discuss the stability and convergence of the difference scheme in the L∞ $L_{\infty}$ norm. To reduce the computational complexity, we introduce a revised Newton method for implementing the difference scheme. Finally, we provide several numerical experiments to support the theoretical results. |
| first_indexed | 2024-12-14T11:08:01Z |
| format | Article |
| id | doaj.art-393690b758ca416e82f21f32c9988078 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-14T11:08:01Z |
| publishDate | 2018-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-393690b758ca416e82f21f32c99880782022-12-21T23:04:26ZengSpringerOpenAdvances in Difference Equations1687-18472018-07-012018112210.1186/s13662-018-1689-5A conservative difference scheme for the Riesz space-fractional sine-Gordon equationZhiyong Xing0Liping Wen1School of Mathematics and Computational Science, Xiangtan UniversitySchool of Mathematics and Computational Science, Xiangtan UniversityAbstract In this paper, we study a conservative difference scheme for the sine-Gordon equation (SGE) with the Riesz space fractional derivative. We rigorously establish the conservation property and solvability of the difference scheme. We discuss the stability and convergence of the difference scheme in the L∞ $L_{\infty}$ norm. To reduce the computational complexity, we introduce a revised Newton method for implementing the difference scheme. Finally, we provide several numerical experiments to support the theoretical results.http://link.springer.com/article/10.1186/s13662-018-1689-5Space-fractional sine-Gordon equationRiesz fractional derivativeConservation lawNewton methodConvergence and stability |
| spellingShingle | Zhiyong Xing Liping Wen A conservative difference scheme for the Riesz space-fractional sine-Gordon equation Advances in Difference Equations Space-fractional sine-Gordon equation Riesz fractional derivative Conservation law Newton method Convergence and stability |
| title | A conservative difference scheme for the Riesz space-fractional sine-Gordon equation |
| title_full | A conservative difference scheme for the Riesz space-fractional sine-Gordon equation |
| title_fullStr | A conservative difference scheme for the Riesz space-fractional sine-Gordon equation |
| title_full_unstemmed | A conservative difference scheme for the Riesz space-fractional sine-Gordon equation |
| title_short | A conservative difference scheme for the Riesz space-fractional sine-Gordon equation |
| title_sort | conservative difference scheme for the riesz space fractional sine gordon equation |
| topic | Space-fractional sine-Gordon equation Riesz fractional derivative Conservation law Newton method Convergence and stability |
| url | http://link.springer.com/article/10.1186/s13662-018-1689-5 |
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