Journal
COMPUTER PHYSICS COMMUNICATIONS
Volume 183, Issue 3, Pages 600-616Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cpc.2011.12.004
Keywords
Two-dimensional sine-Gordon equation; Differential quadrature method; Gauss-Lobatto-Chebyshev grid points; Runge-Kutta method
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During the past few decades, the idea of using differential quadrature methods for numerical solutions of partial differential equations (PDEs) has received much attention throughout the scientific community. In this article, we proposed a numerical technique based on polynomial differential quadrature method (PDQM) to find the numerical solutions of two-dimensional sine-Gordon equation with Neumann boundary conditions. The PDQM reduced the problem into a system of second-order linear differential equations. Then, the obtained system is changed into a system of ordinary differential equations and lastly. RK4 method is used to solve the obtained system. Numerical results are obtained for various cases involving line and ring solitons. The numerical results are found to be in good agreement with the exact solutions and the numerical solutions that exist in literature. It is shown that the technique is easy to apply for multidimensional problems. (C) 2011 Elsevier B.V. All rights reserved.
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