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Approximation of functions in Hölder class by third kind Chebyshev wavelet and its application in solution of Fredholm integro-differential equations

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Abstract

This paper presents numerical solutions to Fredholm integro-differential equations that arise in physical, chemical, engineering, and biological models using approximations by third kind Chebyshev wavelet. A third kind Chebyshev wavelet is used to create an operational matrix, and a method for converting the problem into a system of algebraic equations is proposed. The convergence and error analysis of solution functions in Hölder class using moduli of continuity are also developed. Illustrative examples are provided to demonstrate the effectiveness of the proposed method, and the method is extended to find a solution to a suspension bridge model encountered in engineering.

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Acknowledgements

Shyam Lal, one of the authors, likes to extend his gratitude to DST-CIMS for encouragement to this work. Abhilasha, one of the authors, is grateful to UGC (India) for providing financial assistance in the form of Junior Research Fellowship vide NTA Ref. No. 201610030018 for her research work. The authors thank the reviewers for their time spent on reviewing the manuscript, careful reading and insightful comments and suggestions that lead to improve the quality of this manuscript.

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  1. Abhilasha

    Present address: Department of Mathematics, IIHS, Kurukshetra University, Kurukshetra, India

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  1. Department of Mathematics, Banaras Hindu University, Varanasi, India

    Shyam Lal &  Abhilasha

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Lal, S., Abhilasha Approximation of functions in Hölder class by third kind Chebyshev wavelet and its application in solution of Fredholm integro-differential equations. Rend. Circ. Mat. Palermo, II. Ser 73, 141–160 (2024). https://doi.org/10.1007/s12215-023-00911-6

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