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 A note on time-fractional Navier–Stokes equation and multi-Laplace transform decomposition method

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Hassan Eltayeb ◽  
Imed Bachar ◽  
Yahya T. Abdalla
Keyword(s):  
Numerical Simulation ◽  
Approximate Solution ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equation ◽  
Adomian Decomposition ◽  
Stokes Problems

Abstract In this study, the double Laplace Adomian decomposition method and the triple Laplace Adomian decomposition method are employed to solve one- and two-dimensional time-fractional Navier–Stokes problems, respectively. In order to examine the applicability of these methods some examples are provided. The presented results confirm that the proposed methods are very effective in the search of exact and approximate solutions for the problems. Numerical simulation is used to sketch the exact and approximate solution.

scholarly journals Approximate Method for Solving the Linear Fuzzy Delay Differential Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
S. Narayanamoorthy ◽  
T. L. Yookesh
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Approximate Solution ◽  
Differential Equations ◽  
Approximate Method ◽  
Delay Differential Equations ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Adomian Decomposition ◽  
Delay Differential

We propose an algorithm of the approximate method to solve linear fuzzy delay differential equations using Adomian decomposition method. The detailed algorithm of the approach is provided. The approximate solution is compared with the exact solution to confirm the validity and efficiency of the method to handle linear fuzzy delay differential equation. To show this proper features of this proposed method, numerical example is illustrated.

scholarly journals Approximate solution of nonlinear ordinary differential equation using ZZ decomposition method

2020 ◽  
Vol 4 (1) ◽  
pp. 448-455
Author(s):  
Mulugeta Andualem ◽  
◽  
Atinafu Asfaw ◽  
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Approximate Solution ◽  
Initial Value Problems ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Nonlinear Ordinary Differential Equation ◽  
Initial Value ◽  
Transform Method ◽  
Adomian Decomposition

Nonlinear initial value problems are somewhat difficult to solve analytically as well as numerically related to linear initial value problems as their variety of natures. Because of this, so many scientists still searching for new methods to solve such nonlinear initial value problems. However there are many methods to solve it. In this article we have discussed about the approximate solution of nonlinear first order ordinary differential equation using ZZ decomposition method. This method is a combination of the natural transform method and Adomian decomposition method.

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 An Efficient Analytical Technique, for The Solution of Fractional-Order Telegraph Equations

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 426 ◽  
Author(s):  
Hassan Khan ◽  
Rasool Shah ◽  
Poom Kumam ◽  
Dumitru Baleanu ◽  
Muhammad Arif
Keyword(s):  
Fractional Order ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Analytical Techniques ◽  
Telegraph Equation ◽  
High Rate ◽  
Analytical Technique ◽  
Decomposition Procedure ◽  
Adomian Decomposition ◽  
Telegraph Equations

In the present article, fractional-order telegraph equations are solved by using the Laplace-Adomian decomposition method. The Caputo operator is used to define the fractional derivative. Series form solutions are obtained for fractional-order telegraph equations by using the proposed method. Some numerical examples are presented to understand the procedure of the Laplace-Adomian decomposition method. As the Laplace-Adomian decomposition procedure has shown the least volume of calculations and high rate of convergence compared to other analytical techniques, the Laplace-Adomian decomposition method is considered to be one of the best analytical techniques for solving fractional-order, non-linear partial differential equations—particularly the fractional-order telegraph equation.

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