Numerical Solution of Damped Generalized Regularized Long-Wave (DGRLW) Equation

DOI: 10.5176/2251-1911_CMCGS28

Authors: R. C. Mittal and R. K. Jain

Abstract: In this paper a numerical method is proposed to approximate the solution of the nonlinear damped generalized regularized long-wave (DGRLW) equation with a variable coefficient. The method is based on collocation of quintic B-splines over finite elements so that we have continuity of the dependent variable and its first four derivatives throughout the solution range. We apply quintic B-splines for spatial variable and derivatives which produce a system of first order ordinary differential equations. We solve this system by using SSP-RK3 scheme. This method needs less storage space that causes to less accumulation of numerical errors. The numerical approximate solutions to the nonlinear damped generalized regularized long-wave (DGRLW) equation have been computed without transforming the equation and without using the linearization. Three illustrative examples are included to demonstrate the validity and applicability of the technique. Easy and economical implementation is the strength of this method.

Keywords: nonlinear damped generalized regularized long-wave (DGRLW) equation, quintic B-splines basis functions, SSP-RK3 scheme, Thomas algorithm.