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Numerical approximation of nonlinear stochastic Volterra integral equation based on Walsh function

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Abstract

This paper adopts a highly effective numerical approach for approximating non-linear stochastic Volterra integral equations (NLSVIEs) based on the operational matrices of the Walsh function and the collocation method. The method transforms the integral equation into a system of algebraic equations, which allows for the derivation of an approximate solution. Error analysis is performed, confirming the effectiveness of the proposed method, which results in a linear order of convergence. Numerical examples are provided to illustrate the precision and effectiveness of the proposed method.

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Acknowledgements

The authors would like to thank the reviewers for their helpful suggestions and comments, which improved the quality of this paper.

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Authors and Affiliations

  1. Department of Mathematics, College of Basic Science and Humanities, OUAT, Bhubaneswar, 751003, India

    Prit Pritam Paikaray, Nigam Chandra Parida & Sanghamitra Beuria

  2. School of Mathematics and Computer Science, Iran University of Science and Technology, Tehran, 16846-13114, Iran

    Omid Nikan

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  1. Prit Pritam Paikaray
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  2. Nigam Chandra Parida
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  3. Sanghamitra Beuria
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  4. Omid Nikan
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Correspondence to Omid Nikan.

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Paikaray, P.P., Parida, N.C., Beuria, S. et al. Numerical approximation of nonlinear stochastic Volterra integral equation based on Walsh function. SeMA (2023). https://doi.org/10.1007/s40324-023-00341-5

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