scholarly journals An approximation to the solution of the Brusselator system by Adomian decomposition method and comparing the results with Runge-Kutta method

2007 ◽  
Vol 2 ◽  
pp. 983-989 ◽  
Author(s):  
J. Biazar ◽  
Z. Ayati
Keyword(s):  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Adomian Decomposition ◽  
Runge Kutta

An Approximate Solution of Muijderman's Model for Performance Calculation of Spiral Grooved Gas Seal

2017 ◽  
Vol 139 (5) ◽  
Author(s):  
Wanjun Xu ◽  
Jiangang Yang
Keyword(s):  
Approximate Solution ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Kutta Method ◽  
Film Pressure ◽  
Runge Kutta Method ◽  
Decomposition Procedure ◽  
Adomian Decomposition ◽  
Runge Kutta ◽  
Performance Calculation

This paper presents an approximate solution of Muijderman's model for compressible spiral grooved gas film. The approximate solution is derived from Muijderman's equations by Adomian decomposition method. The obtained approximate solution expresses the gas film pressure as a function of the gas film radius. The traditional Runge–Kutta method is avoided. The accuracy of the approximate solution is acceptable, and it brings convenience for performance calculation of spiral grooved gas seal. A complete Adomian decomposition procedure of Muijderman's equations is presented. The approximate solution is validated with published results.

Application of Adomian Decomposition Method on a Mathematical Model of Malaria

2020 ◽  
pp. 417-435
Author(s):  
Adesoye Idowu Abioye ◽  
Olumuyiwa James Peter ◽  
Ayotunde Abayomi Ayoade ◽  
Ohigweren Airenoni Uwaheren ◽  
Mohammed Olanrewaju Ibrahim
Keyword(s):  
Mathematical Model ◽  
Fourth Order ◽  
Decomposition Method ◽  
Deterministic Model ◽  
Adomian Decomposition Method ◽  
Model Solution ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Adomian Decomposition ◽  
Malaria Model

In this paper, we consider a deterministic model of malaria transmission. Adomian decomposition method (ADM) is used to calculate an approximation to the solution of the non-linear couple of differential equations governing the model. Classical fourth-order Runge-Kutta method implemented in Maple18 confirms the validity of the ADM in solving the problem. Graphical results show that ADM agrees with R-K 4. In order words, these produced the same behaviour, validating ADM's efficiency and accuracy of ADM in finding the malaria model solution.

scholarly journals Approximate Analytical Solution of a Third-Order IVP arising in Thin Film Flows driven by Surface Tension

2017 ◽  
Vol 35 (3) ◽  
pp. 117-129
Author(s):  
Fabrizio Morlando
Keyword(s):  
Analytical Solution ◽  
Approximate Analytical Solution ◽  
Adomian Decomposition Method ◽  
Traveling Wave Solution ◽  
Equation Modeling ◽  
Kutta Method ◽  
Third Order ◽  
Runge Kutta Method ◽  
Adomian Decomposition ◽  
Runge Kutta

In this paper, we present a way of applying the so-called He's variational iteration method (VIM) to numerically solve the non linear autonomous third-order ordinary dierential equation (ODE) y''' = y^-2 obtained by considering a traveling wave solution admitted by a lubrication equation modeling a two-dimensional spreading of a thin viscous lm on a inclined slope. Approximate analytical solution is derived and compared to the results obtained from the Adomian decomposition method (ADM) proposed in [20], to the exact analytical solution[7,8], to a fth order Runge-Kutta method (DOPRI), a fourth order Runge-Kutta method (RK4), a three-stage fth order Runge-Kutta method (RKD5) developed in [18]. A very good agreement and accuracy is observed. Comparisons are obtained using symbolic capabilities of Maple 18.0 package.

scholarly journals Using Adomian decomposition method for solving a vector-host model

2016 ◽  
Vol 5 (2) ◽  
pp. 107
Author(s):  
Ibrahim Elmojtaba
Keyword(s):  
Numerical Methods ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Adomian Decomposition ◽  
Runge Kutta

In this paper, we use Adomian decomposition method (ADM) for solving a vector-host model by using an alternate algorithm suggested by Biazar et. al [4]. Some of the first terms were generated and plotted against time and compared our results with the regular Runge-Kutta numerical methods by using Matlab ode45 function.

scholarly journals Analytical Approximate Solution of Nonlinear Differential Equation Governing Jeffery-Hamel Flow with High Magnetic Field by Adomian Decomposition Method

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
D. D. Ganji ◽  
M. Sheikholeslami ◽  
H. R. Ashorynejad
Keyword(s):  
Decomposition Method ◽  
Hartmann Number ◽  
Adomian Decomposition Method ◽  
Navier Stokes ◽  
Nonlinear Ordinary Differential Equations ◽  
Governing Equations ◽  
Navier Stokes Equation ◽  
Runge Kutta Method ◽  
Adomian Decomposition ◽  
Divergent Channel

The magnetohydrodynamic Jeffery-Hamel flow is studied analytically. The traditional Navier-Stokes equation of fluid mechanics and Maxwell's electromagnetism governing equations reduce to nonlinear ordinary differential equations to model this problem. The analytical tool of Adomian decomposition method is used to solve this nonlinear problem. The velocity profile of the conductive fluid inside the divergent channel is studied for various values of Hartmann number. Results agree well with the numerical (Runge-Kutta method) results, tabulated in a table. The plots confirm that the method used is of high accuracy for different α, Ha, and Re numbers.

scholarly journals Numerical Treatment of the Model for HIV Infection of CD4+T Cells by Using Multistep Laplace Adomian Decomposition Method

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Nurettin Doğan
Keyword(s):  
T Cells ◽  
Hiv Infection ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Computer Code ◽  
Runge Kutta Method ◽  
Adomian Decomposition ◽  
Comparison Of The Results ◽  
Very High

A new method for approximate analytic series solution called multistep Laplace Adomian Decomposition Method (MLADM) has been proposed for solving the model for HIV infection of CD4+T cells. The proposed method is modification of the classical Laplace Adomian Decomposition Method (LADM) with multistep approach. Fourth-order Runge-Kutta method (RK4) is used to evaluate the effectiveness of the proposed algorithm. When we do not know the exact solution of a given problem, generally we use the RK4 method for comparison since it is widely used and accepted. Comparison of the results with RK4 method is confirmed that MLADM performs with very high accuracy. Results show that MLADM is a very promising method for obtaining approximate solutions to the model for HIV infection of CD4+T cells. Some plots and tables are presented to show the reliability and simplicity of the methods. All computations have been made with the aid of a computer code written in Mathematica 7.

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