Abstract
AbstractIn 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 L2 and H1 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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