Numerical Approximation of Stochastic Volterra Integral Equation Using Walsh Function
Numerical Analysis
2024-09-02 v1 Numerical Analysis
Probability
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.
Cite
@article{arxiv.2305.00823,
title = {Numerical Approximation of Stochastic Volterra Integral Equation Using Walsh Function},
author = {Prit Pritam Paikaray and Sanghamitra Beuria and Nigam Chandra Parida},
journal= {arXiv preprint arXiv:2305.00823},
year = {2024}
}