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

Author(s):

Mansour Shiralizadeh * , Amjad Alipanah , Maryam Mohammadi

Message:
Article Type:
Research/Original Article (دارای رتبه معتبر)
Abstract:

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.

Keywords:

Sine-Gordon equation , Radial Basis Function , Rational radial basis function method , Conservation law

Language:
English
Published:
Journal of Mathematical Modeling, Volume:10 Issue: 3, Summer 2022
Pages:
387 to 405
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