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 ...

In this paper a recurrence technique for calculating Adomian polynomials is proposed, the convergence of the series for the Adomian polynomials is discussed, and the dependence of the convergent domain of the solution's decomposition series P 1 n¼0 u n on the initial component function u 0 is illustrated. By introducing the index vectors of the Adomian polynomi-als the recurrence relations of t...

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 ...

This paper successfully applies the Adomian decomposition  and the modified Laplace Adomian decomposition methods to find  the approximate solution of a nonlinear fractional Volterra-Fredholm integro-differential equation. The reliability of the methods and reduction in the size of the computational work give these methods a wider applicability. Also, the behavior of the solution can be formall...

dynamically adaptive numerical methods have been developed to find solutions for differential equations. thesubject of wavelet has attracted the interest of many researchers, especially, in finding efficient solutions fordifferential equations. wavelets have the ability to show functions at different levels of resolution. in this paper, a numerical method is proposed for solving the second pain...

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...

in this work, the solution of a boundary value problem is discussed via asemi analytical method. the purpose of the present paper is to inspect theapplication of the adomian decomposition method for solving the nagumo tele-graph equation. the numerical solution is obtained for some special cases sothat demonstrate the validity of method.

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...

In this paper, the Adomian decomposition method for the approximate solution of generalized Korteweg de Vries equation with boundary conditions is implemented. By using this method, the solution is calculated in the form of power series. The method does not need linearization, weak nonlinearity or perturbation theory. By using Mathematica Program, Adomian polynomials of the obtained series solu...