Numerical solutions of generalized Rosenau-Kawahara-RLW equation using finite element method

Abstract

Nonlinear wave phenomena appear in many fields, such as fluid mechanics, plasma physics, applied mathematics, in engineering problems, biology, hydrodynamics, solid state physics and optical bers. In order to better understand these nonlinear phenomena, it is important to explore their exact solutions. But exact solutions of these equations are commonly not derivable, particularly when the nonlinear terms are contained. In so far as only limited classes of these equations are solved by analytical means, numerical solutions of these nonlinear partial differential equations are very operable to examine physical phenomena [1]. In this work, we have obtained numerical solutions of the generalized RosenauKawahara-RLW equation by using collocation finite element method. To show the effectivity and proficiency of the method, error norms L2, L∞ and invariant IE have been computed. A linear stability analysis based on a Fourier method states that the numerical scheme is unconditionally stable