Numerical solution of one-dimensional Sine-Gordon equation using rational radial basis functions

Document Type : Research Article


1 Department of Applied Mathematics, University of Kurdistan, Sanandaj, Iran

2 Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran


In this paper, we use the rational radial basis function (RRBF) method for solving the one dimensional Sine-Gordon (SG) equation, especially the case with steep front or sharp gradient solutions. The time and spatial derivatives are approximated by the finite difference and RRBF method, respectively. Some numerical experiments are given in both perturbed and unperturbed cases, and are compared with some other numerical methods to confirm the good accuracy of the presented method. The conservation law of energy is also investigated.