Solving FIDEs by Using Semi-Analytical Techniques

Abstract

This paper mainly focuses on the recent advances in the semi-analytical approximated methods for solving Fredholm Integro-Differential Equations (FIDEs) of the second kind by using Variational Iteration Method (VIM), Homotopy Perturbation Method (HPM) and Direct Homotopy Analysis Method (DHAM). Convergence analysis of the exact solution of the proposed methods is established. Moreover, we proved the uniqueness of the solution. To illustrate the methods, an example is presented.

First-order numerical method for the singularly perturbed nonlinear Fredholm integro-differential equation with integral boundary condition

“…Significant efforts have been made in the last 50 years to treat the Volterra/Fredholm integral equations numerically [18,19,20,21,22,23,24,25,26,27,28,29]. More specically, in [30,31], a difference scheme of the exponential type on a uniform mesh is considered.…”

“…In [35,36] a second-order uniformly convergent finite difference schemes are constructed on a Shishkin type mesh. [23] presents a variational iteration method for solving FIDEs. This study provides an analytical approximation to determine the behavior of the solution.…”

Constructing the National Body through Public Homophobia: A Discourse Analysis of Egyptian Media Coverage of the ‘Rainbow Flag Case’ in 2017

“…Under Sisi, the 'January 25 Revolution' became subject to several stages of appropriation and delegitimisation; 31 i.e. regime and media assert that the revolution had catastrophic effects on the economy and state securitya posture aimed at persuading people that any other uprising would be dangerous 32 while simultaneously absolving Sisi from the blame for Egypt's current situation.…”