An Application of the Weighted Mean Value Method to Fredholm integral equations with Toeplitz plus Hankel kernels

In the present work, we study Fredholm integral equations of the second kind with Toeplitz, Hankel, and Toeplitz plus Hankel kernels. The weighted mean-value method is employed and extended to obtain numerical solutions for one-and multidimensional Fredholm integral equations of the second kind. By a successful application of this method, we first convert the integral equation into a system of algebraic equations, then solve this system and obtain promising results. Finally, numerical examples are provided to show the simplicity and applicability of the method.