Hybrid functions approach to solve a class of Fredholm and Volterra integro-differential equations

TL;DR

This paper introduces a numerical hybrid functions method for efficiently solving Fredholm and Volterra integro-differential equations by converting them into algebraic systems, validated through numerical examples.

Contribution

It presents a novel hybrid and block-pulse functions approach that approximates derivatives and reduces complex equations to algebraic systems for easier solution.

Findings

Method effectively solves integro-differential equations

Numerical examples confirm accuracy and efficiency

Approach simplifies complex equations into algebraic form

Abstract

In this paper, we use a numerical method that involves hybrid and block-pulse functions to approximate solutions of systems of a class of Fredholm and Volterra integro-differential equations. The key point is to derive a new approximation for the derivatives of the solutions and then reduce the integro-differential equation to a system of algebraic equations that can be solved using classical methods. Some numerical examples are dedicated for showing efficiency and validity of the method that we introduce.