Numerical solution of linear Fredholm integral equations via two-dimensional modification of hat functions

In this work we approximate the solution of the linear Fredholm integral equations, by means of a new two-dimensional modification of hat functions (2D-MHFs) and a new operational matrix of integration. By this idea, the basic equations will be changed into the associated systems of algebraic equations. Also, an error analysis is provided under several mild conditions. The method is computationally attractive and some numerical examples are provided to illustrate its high accuracy.