Novel and Reliable Techniques for Two‐Dimensional Stochastic Itô–Volterra Fredholm Integral Equations

ABSTRACT This article proposes two novel numerical techniques for solving two‐dimensional stochastic Itô–Volterra Fredholm integral equations. Many two‐dimensional stochastic integral equations present significant challenges for analytical solutions. Consequently, possessing an efficient method to get very precise numerical solutions for these stochastic integral equations is of paramount importance. In this article, two novel numerical techniques based on two‐dimensional wavelets have been successfully introduced to acquire the numerical solutions of the two‐dimensional stochastic Itô–Volterra Fredholm integral equations. This efficient and noteworthy method transforms the stochastic integral equation into a system of algebraic equations, which is then solved using an appropriate numerical technique. Moreover, convergence analysis and the error analysis have also been well established successfully. At the end, some test problems have been presented to illustrate the accuracy, efficiency, simplicity, and plausibility of the proposed techniques.