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

A new approach for solving nonlinear Thomas-Fermi equation based on fractional order of rational Bessel functions

In this paper, the fractional order of rational Bessel functions collocation method (FRBC) to solve Thomas-Fermi equation which is defined in the semi-infinite domain and has singularity at $x = 0$ and its boundary condition occurs at infinity, have been introduced. We solve the problem on semi-infinite domain without any domain truncation or transformation of the domain of the problem to a finite domain. This approach at first, obtains a sequence of linear differential equations by using the quasilinearization method (QLM), then at each iteration solves it by FRBC method. To illustrate the reliability of this work, we compare the numerical results of the present method with some well-known results in other to show that the new method is accurate, efficient and applicable

Solving One-Predator Two-Prey System by using Adomian Decomposition Method / Wan Khairiyah Hulaini Wan Ramli... [et. al]

In this paper, a mathematical model of one-predator two-prey system is discussed. This model is derived from predator-prey Lotka-Volterra model by adding another population of prey into the system. The model derived is a nonlinear system of ODEs. So the approach to this model is different from the linear system of ODEs. With reference to that, Adomian Decomposition Method (ADM) is one of the semi-analytical approaches being applied in this paper to solve the system. The approximate solution is made until four terms. The solution obtained is analyzed graphically

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