Algorithms for Solving Volterra Integral Equations Using Non-Polynomial Spline Function

Abstract

This paper discusses some algorithms for solving Volterra's integral equations of the second degree using non-boundary spline functions, including (linear and cubic), as the linear spline function presents some laws and algorithms of its own, as well as the cubic spline function has its laws and algorithm. They are applied and combined in a language program MATLAB R2022a to find the numerical solution for them and the difference between them through the error percentage that appears for each of them. The preview is done through the drawing, as shown in the examples below.