A hybrid method of block pulse with Bernstein polynomial for numerical solution of linear ill-posed first kind Fredholm Integal equation

Abstract

This study presents an effective method for approximating solutions to first-kind Fredholm integral equations using a hybrid approach combining Block-Pulse and Bernstein polynomials. The  method transforms the integral equation into a system of linear algebraic equations by exploiting the properties of the hybrid functions. Additionally, we estimate the error bound under the L2
norm to assess the accuracy of the approach. To validate the method’s effectiveness, we apply it to some test problems with known exact solutions, demonstrating its reliability and efficiency.