Some Numerical Techniques for Solution of Nonlinear Regularized Long Wave Equation

Abstract

In this study, numerical solutions of the one-dimensional Regularized Long Wave (RLW) equation have been investigated. For this purpose, the RLW equation is divided into two sub equations, one linear and the other nonlinear, according to the time term. Then, algebraic equation systems have been obtained by writing the derivative approximations obtained with the help of cubic trigonometric B-spline base functions and Crank-Nicolson finite difference approximations to the derivatives in each sub-equation. To obtain numerical solutions of the RLW equation, these systems are solved the Strang splitting algorithm, Ext4, and Ext6 techniques created by Richardson extrapolation of the Strang algorithm have used to increase the accuracy of the solutions. In order to investigate the effectiveness of these methods, single solitary wave motion and the interaction of two solitary waves problems, which are most commonly used in the literature, have been taken into consideration. In addition, the stability analysis of the Strang algorithm have been investigated by the von Neumann method.

Keywords

• RLW equation
• Richardson extrapolation
• Strang algorithm
• Ext4 algorithm
• Ext6 algorithm
• Solitary waves.

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