An adaptive splitting algorithm for the sine-Gordon equation

Qin Sheng; David A. Voss; Q. M. Khaliq

doi:10.3934/proc.2005.2005.792

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2005, Volume 2005: 792-797. Doi: 10.3934/proc.2005.2005.792 open access

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An adaptive splitting algorithm for the sine-Gordon equation

1.
Department of Mathematics, Baylor University, Waco, TX76798-7328
2.
Department of Mathematics, Western Illinois University, Macomb, IL 61455
3.
Department of Mathematical Sciences, Middle Tennessee State University, Murfreesboro, Tennessee 37132

Received: August 31, 2004

Revised: February 28, 2005

Published: August 2005

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Abstract

This preliminary investigation concerns an adaptive splitting scheme for the numerical solution of two dimensional sine-Gordon equation. The dispersive wave equation allows for soliton-alike solutions, an ubiquitous phenomenon in a large variety of physical problems. The system of nonlinear differential equations obtained via the method of lines is then attached by a recurrence procedure whose solution yields second order accuracy. The numerical solution of the system is designed using the Peaceman-Rachford splitting to avoid solving a nonlinear system of equations at each step and allows more efficient implementations of the difference scheme.

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Mathematics Subject Classification: Primary: 65M06, 65M20; Secondary: 35Q53.

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