A New Improved Hat Function for Numerical Solution of Linear Fredholm Integral Equations

Farshid Mirzaee, Elham Hadadiyan

Abstract

A new and efcient numerical approach is developed for solving linear Fredholm integral equations. The fundamental
structure of the presented method is based on the modication of hat functions (MHFs) in which a new operational matrix
of integration is introduced. After implementation of our scheme, the solution of the main problem would be transformed
into the solution of a system of linear algebraic equations. Also, an error analysis is provided under several mild conditions.
In addition, examples that illustrate the pertinent features of the method are presented, and the results are discussed.