High-order solution of one-dimensional sine-Gordon equation using compact finite difference and DIRKN methods

Authors:
Akbar Mohebbi;Mehdi Dehghan
Affiliations:
Department of Mathematics, Faculty of Science, University of Kashan, Kashan, Iran;Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Ave., 15914, Tehran, Iran
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2010

Citing 21
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Abstract

In this work we propose a high-order and accurate method for solving the one-dimensional nonlinear sine-Gordon equation. The proposed method is based on applying a compact finite difference scheme and the diagonally implicit Runge-Kutta-Nystrom (DIRKN) method for spatial and temporal components, respectively. We apply a compact finite difference approximation of fourth order for discretizing the spatial derivative and a fourth-order A-stable DIRKN method for the time integration of the resulting nonlinear second-order system of ordinary differential equations. The proposed method has fourth-order accuracy in both space and time variables and is unconditionally stable. The results of numerical experiments show that the combination of a compact finite difference approximation of fourth order and a fourth-order A-stable DIRKN method gives an efficient algorithm for solving the one-dimensional sine-Gordon equation.