A Comparison between Adomian Decomposition and Tau Methods

Abstract

We present a comparison between Adomian decomposition method (ADM) and Tau method (TM) for the integro-differential equations with the initial or the boundary conditions. The problem is solved quickly, easily, and elegantly by ADM. The numerical results on the examples are shown to validate the proposed ADM as an effective numerical method to solve the integro-differential equations. The numerical results show that ADM method is very effective and convenient for solving differential equations than Tao method.

Using An accelerated Technique of The Laplace-Adomian Decomposition Method in Solving A class of Non-linear Integro-differential Equations

“…Hence, there are numerous researchers that interested in studying this type of equations. A comparison was made between Adomian decomposition and tau methods in [1] for finding the solution of Volterra integrodifferential equations. In [2] the author used a combined form of the Laplace transform method with the Adomian decomposition method to get the analytic solution of the non-linear Volterra integro-differential equations of first and second kind.…”

Modification of Laplace Adomian Decomposition Method for Solving Nonlinear Volterra Integral and Integro-differential Equations based on Newton Raphson Formula

“…For solving nonlinear functional equations, Adomian decomposition method was introduced by George Adomian in 1980 [4,19,23]. Basically, the technique provides an infinite series solution of the equation and the nonlinear term is decomposed into an infinite series of Adomian polynomials [1, 2, 5, 6, 8, 10, 14-17, 20, 22-24, 26-29].…”

“…Basically, the technique provides an infinite series solution of the equation and the nonlinear term is decomposed into an infinite series of Adomian polynomials [1, 2, 5, 6, 8, 10, 14-17, 20, 22-24, 26-29]. Several linear and nonlinear ordinary, partial, deterministic and stochastic differential equations are solved easily and adequately by Adomian decomposition method [4,13,14,19,23]. In this work, Laplace transform technique in combination with Adomian decomposition method is presented and modified, which was first studied by Khuri in [14] to solve nonlinear differential equations.…”

“…In [7], the technique was applied on delay differential equations. A comparison was made between Adomian decomposition and tau methods in [4] for finding the solution of Volterra integro-differential equations. Magdy and Mohamed [20] practiced Laplace decomposition method and Pade approximation to get the numerical solution of nonlinear system of partial differential equations.…”

“…Nonlinear Volterra integral equations arise in many scientific fields such as the population dynamics, spread of epidemics and semi-conductor devices [25]. Volterra integro-differential equations also emanated in many physical applications such as biological species coexisting together with increasing and decreasing rates of generating and in engineering applications such as heat transfer, diffusion process in general [3,4,21,24]. Recently, many researchers investigated the solution of these problems.…”