文章基本信息

标题：A Crank–Nicolson finite difference scheme for the Riesz space fractional-order parabolic-type sine-Gordon equation
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作者：Yanjie Zhou ; Zhendong Luo
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2018
卷号：2018
期号：1
页码：216
DOI：10.1186/s13662-018-1674-z
语种：English
出版社：Hindawi Publishing Corporation
摘要：In this paper, we focus on the study of the Crank–Nicolson finite difference (CNFD) scheme for the Riesz space fractional-order parabolic-type sine-Gordon equation (RSFOPTSGE). For this purpose, we first establish the CNFD scheme for RSFOPTSGE. Then, we discuss the existence, uniqueness, stability, and convergence of the CNFD solutions. Finally, we supply a numerical experiment to validate the correctness of theoretical results. This indicates that the CNFD scheme is very effective for solving RSFOPTSGE.
关键词：Crank–Nicolson finite difference scheme ; Riesz space fractional-order parabolic-type sine-Gordon equation ; Existence, stability, and convergence ; Numerical experiment