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arXiv · 2306.06920

Numerical Approximation of Nonlinear Stochastic Volterra Integral Equation using Walsh Function

Prit Pritam Paikaray·Nigam Chandra Parida·Sanghamitra Beuria·Omid Nikan
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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 has been 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 this proposed method.

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Prit Pritam Paikaray, Nigam Chandra Parida, Sanghamitra Beuria, Omid Nikan. 2023-06-12. Numerical Approximation of Nonlinear Stochastic Volterra Integral Equation using Walsh Function. https://doi.org/10.1007/s40324-023-00341-5

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