李晓芳,谢树森

• 1:中国海洋大学数学科学学院

摘要(Abstract)：

本文提出一个解Benjamin方程的高精度显隐多步紧致有限差分格式,即在时间上对线性部分用三阶向后差分隐格式,非线性部分用显格式,空间上采用四阶精度紧致差分格式,最终在时间上和空间上分别达到三阶和四阶精度。证明了半离散紧致差分格式的四阶收敛性,给出了利用快速离散Fourier变换求解全离散格式的数值算法。最后数值算例验证了理论分析结果,并且数值解满足质量守恒定律。

关键词(KeyWords)： Benjamin方程;Hilbert变换;紧致差分法;显隐多步向后差分法

Abstract:

Keywords:

基金项目(Foundation): 中央高校基本科研业务费专项(201562012);; 山东省自然科学基金项目(ZR2017MA016);; 国家重大科技专项(20101010)资助~~

作者(Author): 李晓芳,谢树森

DOI: 10.16441/j.cnki.hdxb.20180055

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