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Chebyshev wavelet approximation of functions having first derivative of H\(\ddot{\text {o}}\)lder’s class

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Abstract

In this paper, the Chebyshev wavelet approximations of a uniformly continuous function f and a functions f whose first derivative \(f'\) of class \(H^\alpha [0,1), 0 < \alpha \le 1\), have been determined. These wavelet estimators are sharper, better and best possible in Wavelet analysis. A new method for solving differential equations by the Chebyshev wavelet method has been proposed. Lane-Emden and third-order pantograph non-linear differential equations have been solved by this method. The solutions of these equations have been compared by their exact solution. It is found that the exact solutions and solutions by the Chebyshev Wavelet method are nearly same. This is a significant achievement in wavelet analysis.

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Acknowledgements

Shyam Lal, one of the authors, is thankful to DST-CIMS for encouragement to this work. Authors are grateful to the referee for his valuable comments and suggestions which improve the quality and presentation of this paper.

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Authors and Affiliations

  1. Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi, 221005, India

    Shyam Lal & Neha Patel

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  1. Shyam Lal
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  2. Neha Patel
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Correspondence to Neha Patel.

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Communicated by Pedro Alberto Morettin.

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Lal, S., Patel, N. Chebyshev wavelet approximation of functions having first derivative of H\(\ddot{\text {o}}\)lder’s class. São Paulo J. Math. Sci. 16, 1355–1381 (2022). https://doi.org/10.1007/s40863-021-00219-2

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  • DOI: https://doi.org/10.1007/s40863-021-00219-2

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