scholarly journals Computation of the General Relativistic Perihelion Precession and of Light Deflection via the Laplace-Adomian Decomposition Method

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Man Kwong Mak ◽  
Chun Sing Leung ◽  
Tiberiu Harko
Keyword(s):  
Decomposition Method ◽  
Series Solution ◽  
Equations Of Motion ◽  
Adomian Decomposition Method ◽  
Compact Objects ◽  
Perihelion Precession ◽  
Schwarzschild Geometry ◽  
Adomian Decomposition ◽  
Wide Range ◽  
General Relativistic

We study the equations of motion of the massive and massless particles in the Schwarzschild geometry of general relativity by using the Laplace-Adomian Decomposition Method, which proved to be extremely successful in obtaining series solutions to a wide range of strongly nonlinear differential and integral equations. After introducing a general formalism for the derivation of the equations of motion in arbitrary spherically symmetric static geometries and of the general mathematical formalism of the Laplace-Adomian Decomposition Method, we obtain the series solution of the geodesics equation in the Schwarzschild geometry. The truncated series solution, containing only five terms, can reproduce the exact numerical solution with a high precision. In the first order of approximation we reobtain the standard expression for the perihelion precession. We study in detail the bending angle of light by compact objects in several orders of approximation. The extension of this approach to more general geometries than the Schwarzschild one is also briefly discussed.

scholarly journals Approximate Solution of Urysohn Integral Equations Using the Adomian Decomposition Method

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Randhir Singh ◽  
Gnaneshwar Nelakanti ◽  
Jitendra Kumar
Keyword(s):  
Approximate Solution ◽  
Error Analysis ◽  
Integral Equations ◽  
Decomposition Method ◽  
Series Solution ◽  
Adomian Decomposition Method ◽  
Numerical Examples ◽  
Recursive Scheme ◽  
Urysohn Integral Equations ◽  
Adomian Decomposition

We apply Adomian decomposition method (ADM) for obtaining approximate series solution of Urysohn integral equations. The ADM provides a direct recursive scheme for solving such problems approximately. The approximations of the solution are obtained in the form of series with easily calculable components. Furthermore, we also discuss the convergence and error analysis of the ADM. Moreover, three numerical examples are included to demonstrate the accuracy and applicability of the method.

scholarly journals A New Computational Approach for Solving Fractional Order Telegraph Equations

2021 ◽  
Vol 13 (3) ◽  
pp. 715-732
Author(s):  
A. Devi ◽  
M. Jakhar
Keyword(s):  
Fractional Order ◽  
Decomposition Method ◽  
Series Solution ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Computational Approach ◽  
Order Problem ◽  
Adomian Decomposition ◽  
Telegraph Equations ◽  
Derivatives Of

In this work, a modified decomposition method namely Sumudu-Adomian Decomposition Method (SADM) is implemented to find the exact and approximate solutions of fractional order telegraph equations. The derivatives of fractional-order are expressed in terms of caputo operator. Some numerical examples are illustrated to examine the efficiency of the proposed technique. Solutions of fractional order telegraph equations are obtained in the form of a series solution. It is observed that the solutions of fractional order telegraph equations converge towards the solution of an integer-order problem, which confirmed the reliability of the suggested method.

scholarly journals Adomian Decomposition Method for a Nonlinear Heat Equation with Temperature Dependent Thermal Properties

2009 ◽  
Vol 2009 ◽  
pp. 1-12 ◽  
Author(s):  
Ashfaque H. Bokhari ◽  
Ghulam Mohammad ◽  
M. T. Mustafa ◽  
F. D. Zaman
Keyword(s):  
Exact Solution ◽  
Heat Equation ◽  
Decomposition Method ◽  
Series Solution ◽  
Adomian Decomposition Method ◽  
Nonlinear Heat Equation ◽  
Temperature Dependent ◽  
Modified Adomian Decomposition Method ◽  
Adomian Decomposition ◽  
Method Analysis

The solutions of nonlinear heat equation with temperature dependent diffusivity are investigated using the modified Adomian decomposition method. Analysis of the method and examples are given to show that the Adomian series solution gives an excellent approximation to the exact solution. This accuracy can be increased by increasing the number of terms in the series expansion. The Adomian solutions are presented in some situations of interest.

scholarly journals EXACT AND APPROXIMATE ANALYTIC SOLUTIONS OF THE JEFFERY-HAMEL FLOW PROBLEM BY THE DUAN-RACH MODIFIED ADOMIAN DECOMPOSITION METHOD

2016 ◽  
Vol 21 (2) ◽  
pp. 174-187 ◽  
Author(s):  
Lazhar Bougoffa ◽  
Samy Mziou ◽  
Randolph C. Rach
Keyword(s):  
Decomposition Method ◽  
Series Solution ◽  
Nonlinear Boundary ◽  
Flow Problem ◽  
Adomian Decomposition Method ◽  
Analytic Solutions ◽  
Series Method ◽  
Power Series Method ◽  
Modified Adomian Decomposition Method ◽  
Adomian Decomposition

This paper aims to find the exact solution in an implicit form for the wellknown nonlinear boundary value problem, namely the MHD Jeffery-Hamel problem, which can be described as the flow between two planes that meet at an angle. Also, two accurate approximate analytic solutions (series solution) are obtained by the variation of the power series method (VPS) and the Duan-Rach modified Adomian decomposition method (DRMA).

scholarly journals Picard and Adomian Solutions of a Nonlocal Cauchy Problem of a Delay Dierential Equation

2021 ◽  
pp. 30-43
Author(s):  
E. A. A. Ziada
Keyword(s):  
Cauchy Problem ◽  
Existence And Uniqueness ◽  
Decomposition Method ◽  
Series Solution ◽  
Adomian Decomposition Method ◽  
Adomian Decomposition ◽  
Uniqueness Of The Solution ◽  
Picard Method ◽  
Delay Differential ◽  
Nonlocal Cauchy Problem

In this paper, two methods are used to solve a nonlocal Cauchy problem of a delay differential equation; Adomian decomposition method (ADM) and Picard method. The existence and uniqueness of the solution are proved. The convergence of the series solution and the error analysis are studied.

scholarly journals Solving Ratio-Dependent Predator-Prey System with Constant Effort Harvesting Using Homotopy Perturbation Method

2008 ◽  
Vol 2008 ◽  
pp. 1-8 ◽  
Author(s):  
Abdoul R. Ghotbi ◽  
A. Barari ◽  
D. D. Ganji
Keyword(s):  
Perturbation Method ◽  
Decomposition Method ◽  
Homotopy Perturbation Method ◽  
Adomian Decomposition Method ◽  
Predator Prey ◽  
Homotopy Perturbation ◽  
Prey System ◽  
Adomian Decomposition ◽  
Wide Range ◽  
Ratio Dependent

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 results show that, in new model, there are less computations needed in comparison to Adomian decomposition method.

scholarly journals An accelerated solution for some classes of nonlinear partial differential equations

2021 ◽  
Vol 29 (1) ◽  
Author(s):  
I. L. El-Kalla ◽  
E. M. Mohamed ◽  
H. A. A. El-Saka
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Decomposition Method ◽  
Series Solution ◽  
Nonlinear Partial Differential Equations ◽  
Adomian Decomposition Method ◽  
Partial Differential ◽  
Adomian Polynomials ◽  
Numerical Examples ◽  
Adomian Decomposition

AbstractIn this paper, we apply an accelerated version of the Adomian decomposition method for solving a class of nonlinear partial differential equations. This version is a smart recursive technique in which no differentiation for computing the Adomian polynomials is needed. Convergence analysis of this version is discussed, and the error of the series solution is estimated. Some numerical examples were solved, and the numerical results illustrate the effectiveness of this version.

Sign in / Sign up

Export Citation Format

Share Document