American Institute of Mathematical Sciences

Advanced
2005, 2005(Special): 792-797. doi: 10.3934/proc.2005.2005.792

An adaptive splitting algorithm for the sine-Gordon equation

Qin Sheng 1, , David A. Voss 2, and  Q. M. Khaliq 3,

1. 

Department of Mathematics, Baylor University, Waco, TX76798-7328, United States
2. 

Department of Mathematics, Western Illinois University, Macomb, IL 61455, United States
3. 

Department of Mathematical Sciences, Middle Tennessee State University, Murfreesboro, Tennessee 37132, United States

Received  September 2004 Revised  March 2005 Published  September 2005

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.
Keywords: numerical stability., sequential splitting, finite difference method, Solitary waves, Adaptation.
Mathematics Subject Classification: Primary: 65M06, 65M20; Secondary: 35Q5.
Citation: Qin Sheng, David A. Voss, Q. M. Khaliq. An adaptive splitting algorithm for the sine-Gordon equation. Conference Publications, 2005, 2005 (Special) : 792-797. doi: 10.3934/proc.2005.2005.792
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