4.5 Article

Barycentric rational interpolation and local radial basis functions based numerical algorithms for multidimensional sine-Gordon equation

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出版社

WILEY
DOI: 10.1002/num.22636

关键词

barycentric rational interpolation; differential quadrature method; local radial basis functions; sine‐ Gordon equation; truncation error and convergence analysis

资金

  1. Council of Scientific and Industrial Research (CSIR) [25(0299)/19/EMR-II]

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This article develops numerical algorithms for solving multidimensional sine-Gordon (SG) equation using barycentric rational interpolation and local radial basis functions. The algorithms involve semi-discretization in time, analysis of truncation errors and convergence, full discretization using two different functions, and solving a linear system with MATLAB routine. Numerical experiments include 1D and 2D SG equations with examples of line and ring solitons, along with a comparative study of results with existing numerical solutions and exact solutions.
In this article, barycentric rational interpolation and local radial basis functions (RBFs) based numerical algorithms are developed for solving multidimensional sine-Gordon (SG) equation. In the development of these algorithms, the first step is to drive a semi-discretization in time with a finite difference, and then the semi-discrete problem is analyzed for truncation errors and convergence in L-2 and H-1 spaces. After that, the semi-discrete system is fully discretized by two different functions, such as barycentric rational and local RBFs. Finally, we obtain a linear system in both the algorithms and the system is solved by a MATLAB routine. In numerical experiments, 1D and 2D SG are considered with various examples of line and ring solitons. Moreover, a comparative study of present results with available numerical ones and exact solutions is also discussed.

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