Numerical Approximation of Nonlinear Stochastic Volterra Integral Equation using Walsh Function

06/12/2023

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by   Prit Pritam Paikaray, et al.

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This article proposes an efficient numerical method for solving nonlinear stochastic Volterra integral equations using the operational matrices of the Walsh function and the collocation method. In this method, a nonlinear stochastic Volterra integral equation is reduced to a system of algebraic equations, which are then solved to obtain an approximation of the solution. Error analysis has been performed, confirming the effectiveness of the methodology, which results in a linear order of convergence. Examples were computed to demonstrate the efficacy and precision of the method.