Numerical simulation of Bratu’s problem using a new form of the Adomian decomposition technique
International Journal of Numerical Methods for Heat & Fluid Flow
ISSN: 0961-5539
Article publication date: 7 March 2023
Issue publication date: 4 May 2023
Abstract
Purpose
This paper aims to discuss a new form of the Adomian decomposition technique for the numerical treatment of Bratu’s type one-dimensional boundary value problems (BVPs). Moreover, the author also addresses convergence and error analysis for the completeness of the proposed technique.
Design/methodology/approach
First, the author discusses the standard Adomian decomposition method and an algorithm based on Duan’s corollary and Rach’s rule for the fast calculation of the Adomian polynomials. Then, a new form of the Adomian decomposition technique is present for the numerical simulation of Bratu’s BVPs.
Findings
The reliability and validity of the proposed technique are examined by calculating the absolute errors of Bratu’s problem for some different values of Bratu parameter λ. Numerical simulation demonstrates that the proposed technique yields higher accuracy than the Bessel collocation and other known methods.
Originality/value
Unlike the other methods, the proposed technique does not need linearization, discretization or perturbation to handle the non-linear problems. So, the results obtained by the present technique are more physically realistic.
Keywords
Acknowledgements
The author expresses their sincere thanks to the Editor in Chief, Editors and Reviewers for their valuable suggestions to revise this manuscript.
Funding: There is no funding available for the publication of this article.
Conflict of interest: The author declares that there is no conflict of interest.
Ethical approval: Not applicable.
Data availability: The data used to support the findings of this study are included within the article.
Citation
Umesh, U. (2023), "Numerical simulation of Bratu’s problem using a new form of the Adomian decomposition technique", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 33 No. 6, pp. 2295-2307. https://doi.org/10.1108/HFF-11-2022-0656
Publisher
:Emerald Publishing Limited
Copyright © 2023, Emerald Publishing Limited