Approximation solution of two-dimensional linear stochastic Volterra integral equation by applying the Haar wavelet

TL;DR

This paper introduces an efficient Haar wavelet-based numerical method for approximating solutions to two-dimensional linear stochastic Volterra integral equations, addressing the challenge of their analytical intractability.

Contribution

The paper presents a novel Haar wavelet approach specifically designed for two-dimensional stochastic Volterra integral equations, expanding numerical solution techniques.

Findings

The method achieves high accuracy in the provided example.

The Haar wavelet approach is computationally efficient.

The approach effectively handles the stochastic nature of the equations.

Abstract

Numerical solution of one-dimensional stochastic integral equations because of the randomness has its own problems, i.e. some of them no have analytically solution or finding their analytic solution is very difficult. This problem for two-dimensional equations is twofold. Thus, finding an efficient way to approximate solutions of these equations is an essential requirement. To begin this important issue in this paper, we will give an efficient method based on Haar wavelet to approximate a solution for the two-dimensional linear stochastic Volterra integral equation. We also give an example to demonstrate the accuracy of the method.