A SPLINE-BASED DIFFERENTIAL QUADRATURE APPROACH TO SOLVE SINE-GORDON EQUATION IN ONE AND TWO DIMENSION

Abstract

This paper endeavors to compute the soliton solution for the sine-Gordon (SG) equation using a hybrid numerical method. The present method has been developed using a modified trigonometric B-spline function with the differential quadrature method (DQM). The method is capable of reducing the partial differential equation into a system of ordinary differential equations which is further stimulated with SSP-RK43, which is a form of the Runge–Kutta method. The present method has been established for its applicability by the numerical simulation of one-soliton and interaction of two solitons for one- and two-dimensional SG equation. The error norms have been calculated and the obtained results are found to approach the exact solutions. The stability of the method is demonstrated with the help of eigenvalues. The results are found encouraging and thus the method can be implemented to solve the similar nonlinear partial differential equations.