Numerical solutions of generalized Rosenau–KDV–RLW equation by using Haar wavelet collocation approach coupled with nonstandard finite difference scheme and quasilinearization

Abstract

In this article, we analyze and propose to compute the numerical solutions of a generalized Rosenau-KDV-RLW (Rosenau-Korteweg De Vries-Regularized Long Wave) equation based on the Haar wavelet (HW) collocation approach coupled with nonstandard finite difference (NSFD) scheme and quasilinearization. In the process of the numerical solution, the NSFD scheme is applied to discretize the first-order time derivative, Haar wavelets are applied on spatial derivatives and the non-linear term is taken care by quasilinearization technique. To discuss the efficiency of the method we compute L ∞ error and L 2 error. We also use discrete mass and energy conservation to check the accuracy of the proposed methodology. The computed results have been compared with the existing methods, for example, three-level average implicit finite difference technique, B-spline collocation, three-level linear conservative implicit finite difference scheme and conservative fourth-order stable finite difference scheme.

Generalized model of stochastic common property fishery differential game: Numerical study

“…. , N in (57), we collocate the residual functions (61) in quadrature nodes (49) for 0 < α < 2 and (50) for α ≥ 2 at s = 1, 2, . .…”

“…Based on the points stated above, we need an appropriate numerical method to solve problems with such characteristics. Due to the high accuracy and ease of implementation, the collocation method is a powerful tool for solving different kinds of differential and integral equations ( Black [9]; Canuto et al [12]; Aguilar, and Brunner [3]; Boyd [10]; Nikooeinejad et al [37]; Jaleb, and Adibi [23]; Nikooeinejad, and Heydari [38]; Verma et al [48]; Verma, and Rawani [49]). Chelyshkov polynomials (CPs) are widely used as basis functions in collocation methods due to theoretical and practical viewpoints in [15].…”