Using Hermite Polynomials to Solve Volterra-Fredholm Integral Equation of the Second Kind

This is the authors' abstract. We don't add key points for this paper.

The objective of this study is to solve Linear Volterra-Fredholm Integral Equations of the second kind numerically using Hermite polynomials.We will present an approximate solution as a series that converges towards the exact solution.Several examples are provided to illustrate the numerical results, specifically comparing the exact and numerical solutions.These comparisons are shown in tables, demonstrating that the error between the exact and numerical solutions is negligible.Additionally, diagrams highlight how closely the numerical solution matches the exact solution, underscoring the accuracy of the grouping method used to solve the Volterra-Fredholm Integral Equation with the MATLAB program.This method is noted for its simplicity, speed, and high accuracy in obtaining numerical results.