Modified Adomian Decomposition Method for Solving Fuzzy Volterra-Fredholm Integral Equation

Abstract

In this paper, a modied Adomian decomposition method has been applied to approximate the solution of the fuzzy Volterra-Fredholm integral equations of the first and second Kind. That, a fuzzy Volterra-Fredholm integral equation has been converted to a system of Volterra-Fredholm integral equations in crisp case. We use MADM to find the approximate solution of this system and hence obtain an approximation for the fuzzy solution of the Fuzzy Volterra-Fredholm integral equation. A nonlinear evolution model is investigated. Moreover, we will prove the existence, uniqueness of the solution and convergence of the proposed method. Also, some numerical examples are included to demonstrate the validity and applicability of the proposed technique.

A Study of Some Reliable Methods for Solving Fuzzy Volterra-Fredholm Integral Equations

“…The modified technique may give the exact solution for nonlinear equations without the necessity to find the Adomian polynomials. We refer the reader to [23,24,30] for more details about the MADM. Accordingly, a slight variation was proposed only on the components u 0 and u 1 .…”

Laplace discrete decomposition method for solving nonlinear Volterra-Fredholm integro-differential equations

“…The integro-differential equations have attracted much more interest of mathematicians and physicists which provides an efficiency for the description of many practical dynamical arising in engineering and scientific disciplines such as, physics, biology, electrochemistry, chemistry, economy, electromagnetic, control theory and viscoelasticity [2,3,5,12,13,15,16,19,[21][22][23]. In recent years, many authors focus on the development of numerical and analytical techniques for fractional integro-differential equations.…”

Variational iterative method: an appropriate numerical scheme for solving system of linear Volterra fuzzy integro-differential equations

“…An iterative technique can explore the output of the dynamical systems that were closer to the exact result. Recently, many researchers have utilized approximate techniques like He's variational iteration, Adomian's decomposition, Laplace transforms, homotopy perturbation techniques and others [1,3,5,6,8,10,14,21]. Here we mainly concentrate on the variational iterative technique by which we study the solution of a linear Volterra fuzzy integro-differential system.…”