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Operational matrix based numerical scheme for the solution of time fractional diffusion equations

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Abstract

This paper presents a numerical method based on an operational matrix of Legendre polynomials for resolving the class of time fractional diffusion (TFD) equations. The operational matrix of fractional order derivatives of the Legendre polynomials is derived as a product of matrices. The collocation method together with the operational matrix of Legendre polynomials are employed to transform the TFD equations into a set of algebraic equations. The perturbation method is applied to show the stability of the discussed method. The accuracy of the suggested method is validated using numerical experiments. The solution obtained by this method is in excellent agreement with the exact solution for the integer order of derivatives and is more precise than the solution obtained by the existing method in which Bernstein polynomials are taken as the basis polynomials.

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Acknowledgements

The authors appreciate the reviewers’ insightful comments. The first author would like to thank the Council of Scientific and Industrial Research Government of India, for financial assistance in the form of research stipend (09/0874(13343)/2022-EMR-I). The authors also thank to Department of Science and Technology, Government of India, for supporting the completion of this work under the "FIST" scheme (No.SR/FST/MS-I/2019/40).

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  1. Department of Mathematics, National Institute of Technology Calicut, Calicut, Kerala, India

    S. Poojitha & Ashish Awasthi

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  1. S. Poojitha
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  2. Ashish Awasthi
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Correspondence to Ashish Awasthi.

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Poojitha, S., Awasthi, A. Operational matrix based numerical scheme for the solution of time fractional diffusion equations. Fract Calc Appl Anal 27, 877–895 (2024). https://doi.org/10.1007/s13540-024-00252-w

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  • DOI: https://doi.org/10.1007/s13540-024-00252-w

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