University of Guilan Journal of Mathematical Modeling 2345-394X 10 3 2022 09 01 Numerical solution of one-dimensional Sine-Gordon equation using rational radial basis functions 387 405 5295 10.22124/jmm.2021.20458.1780 EN Mansour Shiralizadeh Department of Applied Mathematics, University of Kurdistan, Sanandaj, Iran Amjad Alipanah Department of Applied Mathematics, University of Kurdistan, Sanandaj, Iran Maryam Mohammadi Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran Journal Article 2021 08 28 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. Sine-Gordon equation Radial Basis Function Rational radial basis function method Conservation law https://jmm.guilan.ac.ir/article_5295_de9abe4cf0ac24ae91f18572bf0a1e01.pdf