Decomposition method was first introduced by Adomian since the beginning of the 1980’s for solving wide range of problems whose mathematical models yield equation or system of equation involving algebraic, differential, integral and integro-diffrential [1, 2, 3]. This iterative method has been proven to be rather successful in dealing with linear problems as well as nonlinear. Adomian gives the...

In this paper, the Adomian decomposition method (ADM) is applied to obtain the approximate solution of a mathematical model of carcinogenesis which is a Riccati differential equation derived by Moolgavkar and Venzon (see [9]). The numerical solution obtained by this way have been compared with the exact solution which obtained by Moolgavkar and Venzon (see [11]). This comparison show that the (...

In this work, we conduct a comparative study among the combine Laplace transform and modied Adomian decomposition method (LMADM) and two traditional methods for an analytic and approximate treatment of special type of nonlinear Volterra integro-differential equations of the second kind. The nonlinear part of integro-differential is approximated by Adomian polynomials, and the equation is reduce...

In this paper, the Adomian decomposition method with Green’s function (Standard Adomian and Modified Technique) is applied to solve linear and nonlinear tenth-order boundary value problems with boundary conditions defined at any order derivatives. The numerical results obtained with a small amount of computation are compared with the exact solutions to show the efficiency of the method. The res...

In this paper, the restarted Adomian decomposition method (RADM) is presented to establish an accurate approximate analytical solutions for Duffingvan der Pol (DVP) differential equation. The Lindsted’s method (LM) is used to compare the solutions of the RADM with those obtained using the Adomian decomposition method (ADM). The numerical results show that the RADM in identical conditions gives ...

a new modified adomian decomposition method (adm) is utilized to obtain an analytical solution for buckling of the nanocantilever actuators immersed in liquid electrolytes. the nanoactuators in electrolytes are subject to different nonlinear forces including ionic concentration, van der waals, external voltage and electrochemical forces. the duan–rach modified adomian decomposition method is ut...

Due to wide range of interest in use of bioeconomic models to gain insight into the scientific management of renewable resources like fisheries and forestry, homotopy perturbation method is employed to approximate the solution of the ratio-dependent predator-prey system with constant effort prey harvesting. The results are compared with the results obtained by Adomian decomposition method. The ...

first riccati equation with matrix variable coefficients, arising in optimal and robust control approach, is considered. an analytical approximation of the solution of nonlinear differential riccati equation is investigated using the adomian decomposition method. an application in optimal control is presented. the solution in different order of approximations and different methods of approximat...

the work  addressed in this paper is a comparative study between convergence of the  acceleration techniques, diagonal pad'{e} approximants and shanks transforms, on homotopy analysis method  and adomian decomposition method for solving  differential equations of integer and fractional orders.