Solving Volterra-Fredholm integral equations by non-polynomial spline functions

It depends on our information, non-polynomial spline functions have not been applied for solving Volterra- Fredholm integral equations of the second kind yet. In this paper, we want to use such functions for finding approximation solutions of Volterra-Fredholm integral equations. In our approach, the coefficients of the non-polynomial spline were found by solving a system of linear equations. Then, these functions were utilized to reduce the fredholm integral equations to the solution of algebraic equations. Analysis of convergences investigated. Finally, three examples were presented to show the effectiveness of the method. This was done with the help of a computer program that used the Python code program version 3.9.