Correlation between Adomian and Partial Exponential Bell Polynomials

We obtain some recurrence relationships among the partition vectors of the partial exponential Bell polynomials. On using such results, the $n$-th Adomian polynomial for any nonlinear operator can be expressed explicitly in terms of the partial exponential Bell polynomials. Some new identities for the partial exponential Bell polynomials are obtained by solving certain ordinary differential equations using Adomian decomposition method

Taylor Series for Adomian Decomposition Method

In the paper we analyse the exact solutions to scalar PDEs obtained thanks to summable Taylor series provided by Adomian's decomposition method. We propose the modification of the method which makes the calculations of Taylor coefficients easier and more direct. The difference is essential for instance in case of nonautonomous equations and is illustrated by some examplComment: 9 page

The foam drainage equation with time- and space-fractional derivatives solved by the Adomian method

In this paper, by introducing the fractional derivative in the sense of Caputo, we apply the Adomian decomposition method for the foam drainage equation with time- and space-fractional derivative. As a result, numerical solutions are obtained in a form of rapidly convergent series with easily computable components

Numerical Solution of Coupled System of Nonlinear Partial Differential Equations Using Laplace-Adomian Decomposition Method

Aim of the paper is to investigate applications of Laplace Adomian Decomposition Method (LADM) on nonlinear physical problems. Some coupled system of non-linear partial differential equations (NLPDEs) are considered and solved numerically using LADM. The results obtained by LADM are compared with those obtained by standard and modified Adomian Decomposition Methods. The behavior of the numerical solution is shown through graphs. It is observed that LADM is an effective method with high accuracy with less number of components

Laplace Decomposition Method for the System of Linear and Non-Linear Ordinary Differential Equations

In this paper we use Modified form of Adomian’s Decomposition Method Laplace, which is a mixture of Laplace transforms and Adomian’s Decomposition Method called the Laplace Decomposition Method (LDM) to solve the system of ordinary differential equation of the first order and an ordinary differential equation of any order by converting it into a system of differential equation of order one. Some examples are presented to show the ability of the method for linear and non-linear systems of differential equations also present the comparison of their solution with the exact solution through graphically. Keywords: Laplace Transformation, Adomian’s Decomposition Method (ADM), System of differential equation, linear differential equation and non-linear ordinary differential equation

Analytical solutions of orientation aggregation models, multiple solutions and path following with the Adomian decomposition method

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.In this work we apply the Adomian decomposition method to an orientation aggregation problem modelling the time distribution of filaments. We find analytical solutions under certain specific criteria and programmatically implement the Adomian method to two variants of the orientation aggregation model. We extend the utility of the Adomian decomposition method beyond its original capability to enable it to converge to more than one solution of a nonlinear problem and further to be used as a corrector in path following bifurcation problems