Numerical solution of the two-dimensional first kind Fredholm integral equations using a regularized collocation method

In this study, we present an advanced numerical model for solving the 2D first kind Fredholm integral equations, which are well known to be ill-posed problems. This numerical approach is built on the quadrature formula with the Lavrentiev regularization method. Under some essential assumptions, a comprehensive theoretical explanation of the presented numerical approach is provided. Finally, various numerical examples support the theoretical findings and demonstrate the accuracy of our method.