The numerical solution of the nonlinear Klein-Gordon and Sine-Gordon equations using the Chebyshev tau meshless method
The numerical solution of the nonlinear Klein-Gordon and Sine-Gordon equations using the Chebyshev tau meshless method
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DOI：
10.1016/j.cpc.2014.02.002
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发表时间：
2014-05
期刊：
影响因子：
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通讯作者：
Wenting Shao;Xionghua Wu
中科院分区：
文献类型：
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作者：
Wenting Shao;Xionghua Wu
本文利用基于积分-微分的切比雪夫-陶无网格法(CTMMID)研究了一维Klein-Gordon方程和Sine-Gordon方程的数值解。首先，我们应用CTMMID对空间变量和时间变量进行离散化。全CTMMID可以有效地将初始条件和边界条件结合起来。此外，我们还介绍了空间上的区域分解方法(DDM)和时间上的块推进技术，以解决大区间、长时间计算中定义的问题。与已有的一些研究相比，数值结果更准确，计算量更少。
In this work, we study the numerical solutions of one-dimensional Klein–Gordon and Sine–Gordon equations using the Chebyshev tau meshless method based on the integration–differentiation (CTMMID). First, we apply CTMMID to discretize both space and time variables. The initial and boundary conditions could be incorporated efficiently with full CTMMID. Furthermore, we introduce the Domain Decomposition Method (DDM) in space and the block-marching technique in time for problems defined in large interval and long time computing. The numerical results are more accurate and with less computational effort than some existing studies.