We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Numerical solutions of generalized Rosenau–KDV–RLW equation by using Haar wavelet collocation approach coupled with nonstandard finite difference scheme and quasilinearization.
- Authors
Verma, Amit Kumar; Rawani, Mukesh Kumar
- 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∞$$ {L}_{\infty } $$ error and L2$$ {L}_2 $$ 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.
- Subjects
QUASILINEARIZATION; FINITE differences; CONSERVATION of mass; ENERGY conservation; EQUATIONS
- Publication
Numerical Methods for Partial Differential Equations, 2023, Vol 39, Issue 2, p1085
- ISSN
0749-159X
- Publication type
Article
- DOI
10.1002/num.22925