Solving Volterra-Fredholm integral equations by natural cubic spline function

Using the natural cubic spline function, this paper finds the numerical solution of Volterra-Fredholm integral equations of the second kind. The proposed method is based on employing the natural cubic spline function of the unknown function at an arbitrary point and using the integration method to turn the VolterraFredholm integral equation into a system of linear equations concerning to the unknown function. An approximate solution can be easily established by solving the given system. This is accomplished with the help of a computer program that runs on Python 3.9.