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

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.

Numerical Simulation of Generalized Oskolkov Equation via the Septic B-Spline Collocation Method

“…Nonlinear evolution equations (NLEEs) are special classes of the category of partial differential equations (PDEs), which have been studied intensively in past several decades [1]. Various methods [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17] have been devised to find the exact and approximate solutions of PDEs in order to provide more information for understanding physical phenomena arising in numerous scientific and engineering fields such as mathematics, physics, mechanics, biology, ecology, optical fiber, chemical reaction and so on [18].…”

A new energy conservative scheme for regularized long wave equation

“…Therefore, finding its numerical solutions is of practical importance. Various types of methods have been used to solve (1.1), like the H1-Galerkin mixed finite element method [11], the B-spline finite element method [27], [10], [17], [18], finite difference methods [31], [37], the distributed approximating functional method [26], and the Haar wavelet combined with the finite difference method [23]. Moreover, [8], [2], [34], [32], [5], [7], [36], [4] also display interesting numerical results for the RLW equation.…”