Application Of Adomian Decomposition Method Research Articles

Cilia flow of magnetized Eyring-Powell nanofluid in a vertical thermal channel with viscous dissipation: An application of Adomian decomposition method

In this study, authors explore how magnetic fields and the buoyancy force resulting from temperature differences work together. The study is focusing at how an Eyring-Powell nanofluid behaves in a ciliated channel when both natural convection and magnetic effects are at play. A technique called the symplectic metachoronal wave has been used to analyze this analysis. A physical assumption of small Reynolds number is considered to simplify the equations describing the flow rate of the Eyring-Powell nanofluid, making it easier to understand. To get a closed form solution, we have incorporated Adomian decomposition method (ADM). It has been observed that the flow is sped up by 10% with increase in the Eyring-Powell fluid parameter M. The quantity of heat transfer increases with increasing values of the Hartmann, Eyring-Powell fluid parameters, and Brinkmann numbers. This study has implications for bio-inspired engineering, medical applications, and the design of microfluidic devices.

Application of Adomian Decomposition Method for Solving Helmholtz Equation

The Adomian decomposition method (ADM) is effective for solving linear and nonlinear ordinary and partial differential equations, integral equations, algebraic equations and integro-differential equations and it leads to an analytical solution in the form of an infinite power series. We will solve the Helmholtz equation in two dimensional by the Adomian decomposition method.
 Key words: Application of Adomian Decomposition Method, Helmholtz Equation, Adomian Decomposition Method. 

REACTION-DIFFUSION FISHER’S EQUATIONS VIA DECOMPOSITION METHOD

The effect of the source, initial or boundary conditions in the use of Adomian decomposition method (ADM) on nonlinear partial differential equation or nonlinear equation in general is enormous. Sometimes the equation in question result to continuous exact solution in series form, other times it result to discrete approximate analytical solutions. In this paper, we show that continuous exact solitons can be obtained on application of ADM to the Fisher's equation with the deployment Taylor theorem to the terms(s) in question. And, the resulting series is split into the integral equations during the solution process. Resulting to multivariate Taylor's series of the exact solitons with the help of Adomian polynomials of the nonlinear reaction term correctly calculated. More physical results are further depicted in 2D, 3D and contour plots.

Application of Adomian decomposition method to study collision effect in dusty plasma in the presence of polarization force

Application of Adomian decomposition method to study collision effect in dusty plasma in the presence of polarization force

On the Application of Adomian Decomposition Method to Special Equations in Physical Sciences

On the Application of Adomian Decomposition Method to Special Equations in Physical Sciences

Probabilistic interpretations of nonclassic Adomian polynomials

The Adomian decomposition method (ADM) is a powerful tool for solving numerous nonlinear functional equations and a large class of initial/boundary value problems. The main task in the application of ADM is the computation of Adomian polynomials (APs). In addition to classic APs, Rach’s nonclassic APs, called class I-IV polynomials, are used to solve a wide range of nonlinear functional equations. In this paper, we present probabilistic interpretations for the nonclassic APs, including class V polynomials studied by Duan. We derive the recurrence relations for the computation of nonclassic APs using our approach. Some numerical examples are discussed to show that the probabilistic approach to compute the nonclassic APs is attractive and is also simple. Finally, a probabilistic proof is given for the known fact that the class IV APs are the classic APs. The probabilistic approach offers an alternative method to the existing analytical or combinatorial approach.

On the Solutions of Nonlinear Algebraic and Transcendental Equations using Adomian Decomposition Method

This work presents approximate analytical solutions of nonlinear algebraic and transcendental equations through direct applications of Adomian decomposition method. The reliability and efficiency of the method in solving transcendental and nonlinear algebraic equations are demonstrated through different illustrative numerical examples. The method is shown to be conceptually and computationally simple and straightforward without any ambiguity. Also, the method as applied in this study shows that it does not require the development of any other iterative scheme that could be used to find the solution to the nonlinear equations. Additionally, the method does not require finding symbolic or numerical derivatives of any given function. With the use of the Adomian decomposition method, there is no search for an auxiliary parameter for adjusting and controlling the rate and region of convergence of the solution. The method does not require finding the correct fixed point and it is free from the problem of choosing an appropriate initial approximation. Therefore, it is hoped that the present work will assist in providing accurate solutions to many practical problems in science and engineering.

Using Adomian decomposition method for solving systems of second order ordinary differential equations

In this paper, we introduce application of Adomian Decomposition Method (ADM) for solving systems of Ordinary Differential Equations (ODEs). This method is illustrated by four examples of (ODEs) and solutions are obtained. One of the most important advantages of this method is its simplicity in using.

Analytical solution of nonlinear Klein-Gordon equations with cubic nonlinearity by extended Adomian decomposition method

In this paper, we are dedicated to acquire, for the first time, an analytically continuous result of the nonlinear Klein-Gordon equations (NKGE) with cubic nonlinearity via Adomian decomposition method (ADM) using multivariate Taylor’s theorem. These class of equations are nonlinear partial differential equations with initial or boundary conditions being hyperbolic or trigonometric functions. Thus leading to large solution series on application of ADM during the invertible process in the integral equations. Which is often analysed at finite discrete points. To overcome this, we extend the series solution by traditional ADM with the multivariate Taylor’s theorem. The process resulted to a simple solution series that was easier to understand and analysed continuously guaranteeing excellent convergence rate. We demonstrate our findings using four examples that were further depicted pictorially using Maple symbolic software.

Using Adomian decomposition method for solving systems of second order ordinary differential equations

In this paper, we introduce application of Adomian Decomposition Method (ADM) for solving systems of Ordinary Differential Equations (ODEs). This method is illustrated by four examples of (ODEs) and solutions are obtained. One of the most important advantages of this method is its simplicity in using.

Analytical solution of nonlinear Klein-Gordon equations with cubic nonlinearity by extended Adomian decomposition method

In this paper, we are dedicated to acquire, for the first time, an analytically continuous result of the nonlinear Klein-Gordon equations (NKGE) with cubic nonlinearity via Adomian decomposition method (ADM) using multivariate Taylor’s theorem. These class of equations are nonlinear partial differential equations with initial or boundary conditions being hyperbolic or trigonometric functions. Thus leading to large solution series on application of ADM during the invertible process in the integral equations. Which is often analysed at finite discrete points. To overcome this, we extend the series solution by traditional ADM with the multivariate Taylor’s theorem. The process resulted to a simple solution series that was easier to understand and analysed continuously guaranteeing excellent convergence rate. We demonstrate our findings using four examples that were further depicted pictorially using Maple symbolic software.

Application of Adomian Decomposition Method to Solving Higher Order Singular Value Problems for Ordinary Differential Equations

This paper is an attempt to solve singular value problems for higher order ordinary differential equation by using new modification of Adomian Decomposition Method (ADM). Convergent series solution of considered problem have been obtained. Three numerical examples are discussed to validate the strength and ease of the method used.

COMBINED EFFECT OF THERMAL RADIATION AND VISCOUS DISSIPATION ON UNSTEADY FREE CONVECTIVE MAGNETO-HYDRODYNAMIC FLOW THROUGH AN IRREGULAR CHANNEL

This study is focused on the joint effects of thermal radiation and magnetic field on an unsteady flow of natural convective, electrically conducting fluid past an irregular vertical channel in the presence of viscous dissipation. The magnetic field is applied normal to the channel. The coupled ordinary differential equations (ODE) are obtained using perturbation technique on the dimensionless governing equations involving energy and momentum equation. Semi-analytical solutions are obtained for the resultant coupled ODE with the application of Adomian Decomposition Method (ADM) with the aid of Mathematica 11.0 software. The pertinent flow parameters in velocity, temperature, Skin-friction and Nusselt number are discussed and exhibited using tables and graphs. It is revealed that at all regions, thermal radiation and viscous dissipation have a tendency to accelerate the Skin-friction and heat transfer coefficient of the fluid.

Application of Adomian decomposition method to free vibration analysis of thin isotropic rectangular plates submerged in fluid

Investigating dynamic free vibration response of isotropic thin rectangular plate resting on two-parameter elastic foundation is of interest in the field of geotechnics, structure, highway, railway and mechanical engineering. This study employs analytical approach to the investigation of free vibration analysis of isotropic rectangular plate submerged in fluid and resting on combined elastic foundations under different support conditions. The nonlinear partial differential equation of the system is transformed into nonlinear ordinary differential equation using the Galerkin method of separation. The resulting ordinary differential equation is solved using Adomian decomposition method (ADM). The reliability of the solutions obtained is validated with numerical and existing results as reported in the literature. Also, the bending moment and stress are analysed. The analytical solutions are used for the investigation of dynamic behaviour of plates in fluid, effect of aspect ratio, effect of elastic foundation parameters on natural frequency and effect of bending moment and stress on the mode of the vibrating plate. From the results, it is observed that the increase in elastic foundation parameter increases the natural frequency. Increasing the aspect ratio increases the natural frequency. Increasing the combined elastic foundation parameters increases the natural frequency. Natural frequency of plates reduces when submerged in fluid with the mode shapes not significantly affected. The node and antinodes of the mode shapes are affected by moment and stress. It is expected that the present study will add to the existing knowledge in the field of vibration of plates.

Application of Adomian decomposition method to nonlinear systems

In this paper, we study the Adomian decomposition method (ADM for short) including its iterative scheme and convergence analysis, which is a simple and effective technique in dealing with some nonlinear problems. We take algebraic equations and fractional differential equations as applications to illustrate ADM’s efficiency.

Application of Adomian decomposition method to solve the fractional mathematical model of corona virus

The aim of this paper is to solve the fractional mathematical model of Corona Virus by Adomian Decomposition Method. The researchers developed mathematical model which is based on the network Bats-Hosts-Reservoir-People. We used Adomian Decomposition Method to solve the system of time fractional ordinary differential equation. The fractional model is solved numerically by using Caputo fractional derivative and solutions are presented graphically. These solutions may be useful for further research to minimize the infection.

Effect of the Variable Viscosity on the Peristaltic Flow of Newtonian Fluid Coated withMagnetic Field: Application of Adomian Decomposition Method for Endoscope

In the present analysis, peristaltic flow was discussed for MHD Newtonian fluid through the gap between two coaxial tubes, where the viscosity of the fluid is treated as variable. In addition, the inner tube was considered to be at rest, while the outer tube had the sinusoidal wave traveling down its motion. Further, the assumptions of long wave length and low Reynolds number were taken into account for the formulation of the problem. A closed form solution is presented for general viscosity using the Adomian decomposition method. Numerical illustrations that show the physical effects and pertinent features were investigated for different physical included phenomenon. It was found that the pressure rise increases with an increase in Hartmann number, and frictional forces for the outer and inner tube decrease with an increase in Hartmann number when the viscosity is constant. It was also observed that the size of the trapping bolus decreases with an increase in Hartmann number, and increases with an increase in amplitude ratio when the viscosity is parameter.

Convergence of numerical schemes for the solution of partial integro-differential equations used in heat transfer

Integro-differential equations play an important role in may physical phenomena. For instance, it appears in fields like fluid dynamics, biological models and chemical kinetics. One of the most important physical applications is the heat transfer in heterogeneous materials, where physician are looking for efficient methods to solve their modeled equations. The difficulty of solving integro-differential equations analytically made mathematician to search about efficient methods to find an approximate solution. The present article is designed to supply numerical solution of a parabolic Volterra integro-differential equation under initial and boundary conditions. We have made an attempt to develop a numerical solution via the use of Sinc-Galerkin method, the convergence analysis via the use of fixed point theory has been discussed, and showed to be of exponential order. For comparison purposes, we approximate the solution of integro-differential equation using Adomian decomposition method. Sometimes, the Adomian decomposition method is a highly efficient technique used to approximate analytical solution of differential equations, applicability of Adomian decomposition method to partial integro-differential equations has not been studied in details previously in the literatures. In addition, we present numerical examples and comparisons to support the validity of these proposed methods.

Adomian decomposition method to magnetohydrodynamics natural convection heat generating/absorbing slip flow through a porous medium

PurposeThe purpose of this paper is to analyze magnetohydrodynamics fully developed natural convection heat-generating/absorbing slip flow through a porous medium. Adomian decomposition method was applied to find the solutions to the problem.Design/methodology/approachIn this study, Adomian decomposition method was used.FindingsResults show that heat generation parameter enhanced the temperature and velocity of the fluid in the annulus. Moreover, slip effect parameter increases the velocity of the fluid.Originality/valueOriginality is in the application of Adomian decomposition method which allowed the slip at interface.

A modified decomposition method to solve linear elliptic partial differential equations in anisotropic domains by enhancing isotropic responses

A modified version of Adomian decomposition method is presented and applied to solve linear elliptic differential equations in anisotropic domains in a recursive manner. A complementary constitutive decomposition, guided by a constitutive hierarchy, governs the superposition of the operator—a step of the Adomian’s method—and is defined as the original constitutive tensor being constructed by an isotropic tensor added to an anisotropic one. The recursive system obtained by the application of Adomian decomposition method is related to an enhancement of the problem’s isotropic solution by the domain’s anisotropy. Alternative solution procedures as Rayleigh–Ritz and and finite element methods are considered. Requirements for absolute convergence are presented and are related to the decomposition as well as to the material’s anisotropy. The rate of convergence is close related to the eigenvalues of the decomposed constitutive terms. The methodology is demonstrated for two- and three-dimensional of heat conduction, two- and three-dimensional elasticity problems and for homogeneous and heterogeneous thin and thick plates. Numeric and semi-analytic results are presented generalised plane stress elasticity as well as for anisotropic thin and laminated thick plates.