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

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.

Automated summary

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.