Numerical Approximation of Stochastic Volterra Integral Equation Using Walsh Function

Prit Pritam Paikaray; Sanghamitra Beuria; Nigam Chandra Parida

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arXiv · 2305.00823

Numerical Approximation of Stochastic Volterra Integral Equation Using Walsh Function

Prit Pritam Paikaray·Sanghamitra Beuria·Nigam Chandra Parida

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Abstract

This paper provides a numerical approach for solving the linear stochastic Volterra integral equation using Walsh function approximation and the corresponding operational matrix of integration. A convergence analysis and error analysis of the proposed method for stochastic Volterra integral equations with Lipschitz functions are presented. Numerous examples with available analytical solutions demonstrate that the proposed method solves linear stochastic Volterra integral equations more precisely than existing techniques. In addition, the numerical behaviour of the method for a problem with no known analytical solution is demonstrated.

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Prit Pritam Paikaray, Sanghamitra Beuria, Nigam Chandra Parida. 2023-05-01. Numerical Approximation of Stochastic Volterra Integral Equation Using Walsh Function. https://arxiv.org/abs/2305.00823

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