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A new effective coherent numerical technique based on shifted Vieta–Fibonacci polynomials for solving stochastic fractional integro-differential equation

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Abstract

In this article, an operational matrix method based on shifted Vieta–Fibonacci polynomials is utilised to find the numerical solution of fractional order stochastic integro-differential equations. In this method, the operational matrices are developed by using the shifted Vieta–Fibonacci polynomials for the fractional order Caputo differential operator in order to solve the present concerned problem. Using Newton cotes nodes as collocation points, operational matrices are employed to convert the above-mentioned equation into a system of linear algebraic equations. The coherent procedure for the appropriate numerical technique is described in this article. Additionally, the convergence analysis and error bound of the suggested method are well established. In order to illustrate the effectiveness, consistency, plausibility, and reliability of the proposed technique, three numerical examples are given. Moreover, the results obtained by the proposed method have been compared with those obtained by the Chelyshkov operational matrix method.

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Acknowledgements

This research work was financially supported by NBHM, Mumbai, under Department of Atomic Energy, Government of India vide Grant Ref. no. 02011/4/2021 NBHM(R.P.)/R &D II/6975 dated 17/06/2021.

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Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology, Rourkela, 769008, India

    Reema Gupta & S. Saha Ray

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  1. Reema Gupta
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  2. S. Saha Ray
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Correspondence to S. Saha Ray.

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Communicated by Vasily E. Tarasov.

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Gupta, R., Saha Ray, S. A new effective coherent numerical technique based on shifted Vieta–Fibonacci polynomials for solving stochastic fractional integro-differential equation. Comp. Appl. Math. 42, 256 (2023). https://doi.org/10.1007/s40314-023-02398-4

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