Solving the Generalized Regularized Long Wave Equation Using a Distributed Approximating Functional Method

Author:

Pindza Edson1ORCID,Maré Eben1

Affiliation:

1. Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 002, South Africa

Abstract

The generalized regularized long wave (GRLW) equation is solved numerically by using a distributed approximating functional (DAF) method realized by the regularized Hermite local spectral kernel. Test problems including propagation of single solitons, interaction of two and three solitons, and conservation properties of mass, energy, and momentum of the GRLW equation are discussed to test the efficiency and accuracy of the method. Furthermore, using the Maxwellian initial condition, we show that the number of solitons which are generated can be approximately determined. Comparisons are made between the results of the proposed method, analytical solutions, and numerical methods. It is found that the method under consideration is a viable alternative to existing numerical methods.

Funder

Brad Welch

Publisher

Hindawi Limited

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