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An adaptive splitting algorithm for the sine-Gordon equation

Pages: 792 - 797, Issue Special, August 2005

 Abstract        Full Text (6546.4K)              

Qin Sheng - Department of Mathematics, Baylor University, Waco, TX76798-7328, United States (email)
David A. Voss - Department of Mathematics, Western Illinois University, Macomb, IL 61455, United States (email)
Q. M. Khaliq - Department of Mathematical Sciences, Middle Tennessee State University, Murfreesboro, Tennessee 37132, United States (email)

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.

Keywords:  Solitary waves, finite difference method, Adaptation, sequential splitting, numerical stability.
Mathematics Subject Classification:  Primary: 65M06, 65M20; Secondary: 35Q53.

Received: September 2004;      Revised: March 2005;      Published: September 2005.