https://doi.org/10.1140/epjp/s13360-024-05283-z
Regular Article
A superconvergent numerical method under the Fibonacci wavelets for solving the system of nonlinear singular Lane–Embden-type equations
Applied Sciences and Humanities Department, Institute of Engineering and Technology, An Autonomous Constituent Institute of Dr. A.P.J. Abdul Kalam Technical University, 226021, Lucknow, U.P., India
Received:
30
June
2023
Accepted:
15
May
2024
Published online:
10
June
2024
In this study, we present a rapid and efficient approach for solving singular linear and nonlinear Lane–Emden-type differential equations using the Fibonacci wavelet method and collocation technique. We convert these problems into a series of computational equations by employing truncated Fibonacci wavelet expansions and an integration operational matrix. Our proposed Fibonacci wavelet technique undergoes convergence analysis, focusing on the uniform convergence of function expansions. Illustrative examples are provided to demonstrate the superiority of this method over existing approaches. We include figures and tables to compare solution accuracy and error variations. MATLAB software is utilized for all computational tasks.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
