Sobolev方程的一个紧致差分格式
A Compact Finite Difference Scheme for Sobolev Equations
DOI: 10.12677/PM.2017.71001, PDF, HTML, XML, 下载: 1,538  浏览: 1,830 
作者: 经 鑫*, 张鲁明：南京航空航天大学理学院，江苏 南京
关键词: Sobolev方程；紧致差分格式；收敛性；Sobolev Equations； Compact Finite Difference Scheme； Convergence
摘要: 本文对Sobolev方程提出了一个紧致差分格式。并用能量方法证明了该差分格式是以无穷模范数无条件收敛和稳定的，收敛阶为O (τ2+h4) 。数值实验结果验证了理论分析的正确性。
Abstract: A compact finite difference scheme is presented for Sobolev equations. It is proved by the discrete energy method that the compact scheme is unconditionally stable and convergent in norm, and the order of convergence is O (τ2+h4) . The numerical experiment results show that the theory is accurate.
文章引用：经鑫, 张鲁明. Sobolev方程的一个紧致差分格式[J]. 理论数学, 2017, 7(1): 1-9. http://dx.doi.org/10.12677/PM.2017.71001

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