Our aim in this piece of work is to demonstrate the power of the Laplace Adomian decomposition method (LADM) in approximating the solutions of nonlinear differential equations governing the two-dimensional viscous flow induced by a shrinking sheet. Keywords—Adomian polynomials, Laplace Adomian decomposition method, Padé Approximant, Shrinking sheet.

in this paper, we use modified laplace decomposition method to solving initial value problems (ivp) of the second order ordinary differential equations. theproposed method can be applied to linear and nonlinearproblems

‎‎in this article‎, ‎a new method is introduced to give approximate solution to van der pol equation‎. ‎the proposed method is based on the combination of two different methods‎, ‎the spectral adomian decomposition method (sadm) and piecewise method‎, ‎called the piecewise adomian decomposition method (psadm)‎. ‎the numerical results obtained from the proposed method show that this method is an...

In this article we review the Adomian decomposition method (ADM) and its modifications including different modified and parametrized recursion schemes, the multistage ADM for initial value problems as well as the multistage ADM for boundary value problems, new developments of the method and its applications to linear or nonlinear and ordinary or partial differential equations, including fractio...

Here, a simple method to determine the rate of convergence of Adomian decomposition method is introduced. The proposed method is used to compare between the rate of convergence of standard and modified (proposed by Wazwaz [A.M. Wazwaz, A new method for solving singular initial value problems in the second-order ordinary differential equations, Appl. Math. Comput. 128 (2002) 45–57]) Adomian meth...

In this paper, the modified Adomian s decomposition method for calculating a numerical solution of the one-dimensional quasi-linear, the Burgers equation, is presented. Time discretization has been used in decomposition, without using any transformation in the Burgers equation such as Hopf–Cole transformation. The numerical results obtained by this way for various values of viscosity have been ...

This present study developed a new Modified Adomian Decomposition Method (MADM) for integro-differential equations. The modification was carried out by decomposing the source term function into series. terms in series were then selected pairs to form initials prevailing approximation. newly modified decomposition method accelerates convergence of solution faster than Standard (SADM). recommends...

A numerical method based on the Adomian decomposition method which has been developed by Adomian [Adomian, G. (1994). Solving Frontier Problems of Physics: The Decomposition Method. Kluwer Academic Publishers, Boston, MA] is introduced in this paper for the approximate solution of delay differential equation (DDE). The algorithm is illustrated by studying an initial value problem. The results o...

Reduced Differental Transform Method (RDTM), which is one of the useful and effective numerical method, is applied to solve nonlinear time-dependent Foam Drainage Equation (FDE) with different initial conditions. We compare our method with the famous Adomian Decomposition and Laplace Decomposition Methods. The obtained results demonstrated that RDTM is a powerful tool for solving nonlinear part...