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Turkish Journal of Mathematics

AYHAN AYDIN

DOI

10.3906/mat-1901-110

Abstract

A new convergent two-level finite difference scheme is proposed for the numerical solution of initial value problem of the generalized Rosenau--KdV--RLW equation. The new scheme is second-order, linear, conservative, and unconditionally stable. It contains one free parameter. The impact of the parameter to error of the numerical solution is studied. The prior estimate of the finite difference solution is obtained. The existence, uniqueness, and convergence of the scheme are proved by the discrete energy method. Accuracy and reliability of the scheme are tested by simulating the solitary wave graph of the equation. Wave generation subject to initial Gaussian condition has been studied numerically. Different wave generations are observed depending on the dispersion coefficients and the nonlinear advection term. Numerical experiments indicate that the present scheme is conservative, efficient, and of high accuracy, and well simulates the solitary waves for a long time.

Keywords

Rosenau-KdV-RLW equation, conservative finite difference scheme, convergence, a priori error estimate

First Page

2226

Last Page

2245

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