Laplace residual power series method for the numerical solution of time-fractional Newell–Whitehead–Segel model
International Journal of Numerical Methods for Heat & Fluid Flow
ISSN: 0961-5539
Article publication date: 15 February 2023
Issue publication date: 19 May 2023
Abstract
Purpose
This study aims to investigate the approximate solution of the time fractional time-fractional Newell–Whitehead–Segel (TFNWS) model that reflects the appearance of the stripe patterns in two-dimensional systems. The significant results of plot distribution show that the proposed approach is highly authentic and reliable for the fractional-order models.
Design/methodology/approach
The Laplace transform residual power series method (ℒT-RPSM) is the combination of Laplace transform (ℒT) and residual power series method (RPSM). The ℒT is examined to minimize the order of fractional order, whereas the RPSM handles the series solution in the form of convergence. The graphical results of the fractional models are represented through the fractional order α.
Findings
The derived results are obtained in a successive series and yield the results toward the exact solution. These successive series confirm the consistency and accuracy of ℒT-RPSM. This study also compares the exact solutions with the graphical solutions to show the performance and authenticity of the visual solutions. The proposed scheme does not require the restriction of variables and produces the numerical results in terms of a series. This strategy is capable to handle the nonlinear terms very easily for the TFNWS model.
Originality/value
This paper presents the original work. This study reveals that ℒT can perform the solution of fractional-order models without any restriction of variables.
Keywords
Acknowledgements
This work was supported by the Foundation of Yibin University, China (Grant No. 2019QD07).
Citation
Luo, X. and Nadeem, M. (2023), "Laplace residual power series method for the numerical solution of time-fractional Newell–Whitehead–Segel model", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 33 No. 7, pp. 2377-2391. https://doi.org/10.1108/HFF-01-2023-0001
Publisher
:Emerald Publishing Limited
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