Solving Fredholm integro-differential equations using Hybrid and Block-Pulse functions

TL;DR

This paper introduces a novel approach using hybrid and block-pulse functions to efficiently approximate solutions for Fredholm integro-differential equations, demonstrating improved accuracy and computational simplicity over existing methods.

Contribution

The paper presents a new hybrid and block-pulse functions method for solving Fredholm integro-differential equations, converting them into algebraic systems for easier solution.

Findings

Method effectively approximates solutions with high accuracy.

Results outperform Hemeda's original method.

Approach simplifies solving complex integro-differential equations.

Abstract

In this paper, hybrid and block-pulse functions are used to approximate the solution of a class of Fredholm integro-differential equations that was first studied by Hemeda. By employing suitable approximations, the equation has been converted into a system of algebraic equations that can be solved with classical methods. Finally, the method is explained with illustrative examples and results are compared to the results obtained by Hemeda's method to show the usefulness and efficiency of the block-pulse and hybrid functions approach.