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A numerical technique based on Legendre wavelet for linear and nonlinear hyperbolic telegraph equation

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Abstract

This study is devoted to the numerical investigation of linear and nonlinear hyperbolic telegraph equation. We have proposed a wavelet collocation method based on Legendre polynomials for approximating the solution. Both the spatial and temporal variables, along with their derivatives, are approximated using the Legendre wavelet and its integration. The present approach is simple, consistent and straightforward. To assure the theoretical consistency of the method, an estimate for the upper bound of the error norm is provided. We have proved an exponential order of convergence which is better than the methods available in the literature. Some numerical experiments are carried out to justify the theoretical results and the outcomes confirm the computational efficiency of the proposed method.

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Acknowledgements

The authors are thankful to the Editor and the anonymous reviewers for their constructive and fruitful comments which improved the presentation and quality of the paper.

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Authors and Affiliations

  1. Department of Mathematics, Maulana Azad National Urdu University, Hyderabad, Telangana, 500032, India

    Basharat Hussain

  2. Department of Mathematics, National Institute of Technology Andhra Pradesh, Tadepalligudem, Andhra Pradesh, 534101, India

    Mo Faheem

  3. Department of Mathematics, Jamia Millia Islamia, New Delhi, Delhi, 110025, India

    Arshad Khan

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  1. Basharat Hussain
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Hussain, B., Faheem, M. & Khan, A. A numerical technique based on Legendre wavelet for linear and nonlinear hyperbolic telegraph equation. J. Appl. Math. Comput. (2024). https://doi.org/10.1007/s12190-024-02098-0

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