Numerical Approximation of Nonlinear Stochastic Volterra Integral Equation using Walsh Function
Numerical Analysis
2023-11-30 v2 Numerical Analysis
Probability
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.
Cite
@article{arxiv.2306.06920,
title = {Numerical Approximation of Nonlinear Stochastic Volterra Integral Equation using Walsh Function},
author = {Prit Pritam Paikaray and Nigam Chandra Parida and Sanghamitra Beuria and Omid Nikan},
journal= {arXiv preprint arXiv:2306.06920},
year = {2023}
}
Comments
arXiv admin note: substantial text overlap with arXiv:2305.16678, arXiv:2305.00823