Haar wavelets collocation method for a system of nonlinear singular differential equations
ISSN: 0264-4401
Article publication date: 8 August 2020
Issue publication date: 8 February 2021
Abstract
Purpose
The purpose of this paper is to propose an efficient computational technique, which uses Haar wavelets collocation approach coupled with the Newton-Raphson method and solves the following class of system of Lane–Emden equations:
Design/methodology/approach
To deal with singularity, Haar wavelets are used, and to deal with the nonlinear system of equations that arise during computation, the Newton-Raphson method is used. The convergence of these methods is also established and the results are compared with existing techniques.
Findings
The authors propose three methods based on uniform Haar wavelets approximation coupled with the Newton-Raphson method. The authors obtain quadratic convergence for the Haar wavelets collocation method. Test problems are solved to validate various computational aspects of the Haar wavelets approach. The authors observe that with only a few spatial divisions the authors can obtain highly accurate solutions for both initial value problems and boundary value problems.
Originality/value
The results presented in this paper do not exist in the literature. The system of nonlinear singular differential equations is not easy to handle as they are singular, as well as nonlinear. To the best of the knowledge, these are the first results for a system of nonlinear singular differential equations, by using the Haar wavelets collocation approach coupled with the Newton-Raphson method. The results developed in this paper can be used to solve problems arising in different branches of science and engineering.
Keywords
Acknowledgements
Miss Diksha Tiwari is supported by grant P30407 of the Austrian Science Fund FWF. Authors are thankful to anonymous reviewers for the valuable suggestion which has helped us to improve the language and presentation of the paper.
Citation
Verma, A.K., Kumar, N. and Tiwari, D. (2021), "Haar wavelets collocation method for a system of nonlinear singular differential equations", Engineering Computations, Vol. 38 No. 2, pp. 659-698. https://doi.org/10.1108/EC-04-2020-0181
Publisher
:Emerald Publishing Limited
Copyright © 2020, Emerald Publishing Limited