Barycentric rational interpolation and local radial basis functions based numerical algorithms for multidimensional <scp>sine‐Gordon</scp> equation

Ram Jiwari

2020Numerical Methods for Partial Differential Equations41 citationsDOI

Abstract

Abstract 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.

Topics & Concepts

Barycentric coordinate systemMathematicsDiscretizationInterpolation (computer graphics)Radial basis functionNumerical analysisConvergence (economics)Basis functionBasis (linear algebra)AlgorithmApplied mathematicsMathematical analysisGeometryComputer scienceArtificial neural networkEconomicsAnimationEconomic growthMachine learningComputer graphics (images)Numerical methods in engineeringNonlinear Waves and SolitonsNumerical methods for differential equations