Two-Dimensional Uniform and Non-Uniform Haar Wavelet Collocation Approach for a Class of Nonlinear PDEs

Author:

Kumar Narendra1ORCID,Verma Amit K.2ORCID,Agarwal Ravi P.3ORCID

Affiliation:

1. Department of Mathematics, Indian Institute of Technology Jodhpur, Jodhpur 342030, Rajasthan, India

2. Department of Mathematics, Indian Institute of Technology Patna, Bihta, Patna 801106, India

3. Department of Mathematics, Texas A & M University-Kingsville, 700 University Blvd., MSC 172, Kingsville, TX 78363-8202, USA

Abstract

In this paper, we introduce a novel approach employing two-dimensional uniform and non-uniform Haar wavelet collocation methods to effectively solve the generalized Burgers–Huxley and Burgers–Fisher equations. The demonstrated method exhibits an impressive quartic convergence rate. Several test problems are presented to exemplify the accuracy and efficiency of this proposed approach. Our results exhibit exceptional accuracy even with a minimal number of spatial divisions. Additionally, we conduct a comparative analysis of our results with existing methods.

Publisher

MDPI AG

Subject

Applied Mathematics,Modeling and Simulation,General Computer Science,Theoretical Computer Science

Reference64 articles.

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3. Comparative analysis of variational iteration method and Haar wavelet method for the numerical solutions of Burgers–Huxley and Huxley equations;Gupta;J. Math. Chem.,2014

4. A numerical solution of the Generalized Burgers-Huxley Equation by spectral collocation method;Javidi;Appl. Math. Comput.,2006

5. Spectral collocation method and Darvishi’s preconditionings to solve the Generalized Burgers-Huxley Equation;Darvishi;Commun. Nonlinear Sci. Numer. Simul.,2008

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