Adomian Decomposition and Variational Iteration Methods for Solving a Problem Arising in Modelling of Biological Species Living Together

2011 ◽  
Vol 66a ◽  
pp. 93
Author(s):  
Tatari M. ◽  
Haghighi M. ◽  
Dehghan M.
Keyword(s):  
Biological Species ◽  
Variational Iteration ◽  
Adomian Decomposition ◽  
Living Together ◽  
Iteration Methods

Adomian Decomposition and Variational Iteration Methods for Solving a Problem Arising in Modelling of Biological Species Living Together

2011 ◽  
Vol 66 (1-2) ◽  
pp. 93-105
Author(s):  
Mehdi Tatari ◽  
Mahboobeh Haghighi ◽  
Mehdi Dehghan
Keyword(s):  
Decomposition Method ◽  
Analytical Techniques ◽  
Main Property ◽  
High Accuracy ◽  
Biological Species ◽  
Variational Iteration ◽  
Adomian Decomposition ◽  
Living Together ◽  
Iteration Methods ◽  
Iteration Technique

Adomian decomposition and He’s variational iteration methods are analytical techniques, which can be used for solving various kinds of problems. The main property of these methods is in their flexibility and ability to solve nonlinear equations accurately. In this paper, the decomposition method and the variational iteration technique are explained, and their merits as well as their drawbacks are discussed. Then a new implementation of these methods is proposed, which yields an approximate solution with high accuracy in large regions and less computational efforts. A system of integro differential equations arising in modelling of the biological species [1] living together is employed to show how these techniques work efficiently.

APPLICATION OF HOMOTOPY PERTURBATION AND VARIATIONAL ITERATION METHODS TO SIR EPIDEMIC MODEL

2011 ◽  
Vol 11 (01) ◽  
pp. 149-161 ◽  
Author(s):  
ABDOUL R. GHOTBI ◽  
A. BARARI ◽  
M. OMIDVAR ◽  
G. DOMAIRRY
Keyword(s):  
Vaccine Coverage ◽  
Adomian Decomposition Method ◽  
Variational Iteration Method ◽  
Sir Epidemic Model ◽  
Childhood Diseases ◽  
Variational Iteration ◽  
Homotopy Perturbation ◽  
Sir Epidemic ◽  
Adomian Decomposition ◽  
Iteration Methods

Children born are susceptible to various diseases such as mumps and chicken pox. These diseases are the most common form of infectious diseases. In recent years, scientists have been trying to devise strategies to fight against these diseases. Since vaccination is considered the most effective strategy against childhood diseases, the development of the framework that would predict the optimal vaccine coverage level needed to prevent the spread of diseases is crucial. The SIR model is a standard compartmental model that has been used to describe many epidemiological diseases. In this article, two methods namely homotopy perturbation method (HPM) and variational iteration method (VIM) are employed to compute an approximation to the solution of nonlinear system of differential equations governing the problem. The obtained results are compared with those obtained by Adomian decomposition method (ADM). This research reveals that although the obtained results are the same, HPM and VIM are much more robust, more convenient and efficient in comparison to ADM.

scholarly journals Modelling of natural growth with memory effect in economics: An application of adomian decomposition and variational iteration methods

2022 ◽  
Vol 11 (1) ◽  
pp. 73-80 ◽  
Author(s):  
Muhamad Deni Johansyah ◽  
Asep K. Supriatna ◽  
Endang Rusyaman ◽  
Jumadil Saputra
Keyword(s):  
Differential Equation ◽  
Memory Effect ◽  
Adomian Decomposition Method ◽  
Output Growth ◽  
Time Interval ◽  
Natural Growth ◽  
Variational Iteration ◽  
Adomian Decomposition ◽  
Iteration Methods ◽  
With Memory

The power-law memory effect is taken into consideration in a generalisation of the economic model of natural growth. The memory effect refers to a process's reliance on its current state and its history of previous changes. However, the study that focuses on natural growth in economics considering the memory effect with fractional order-linear differential equation model is still limited. The current investigation seeks to solve the natural growth with memory effect in the economics model and decide the best model using fractional differential equation (FDE), namely Adomian Decomposition and Variational Iteration Methods. Also, this study assumes the level of consumer loss memory during a certain time interval denoted by a parameter (α). This study showed the model of loss memory effect with 0 < α ≤ 1 given a slowdown in output growth compared to a model without memory effect. Besides that, this study also found that output Y(t) is growing faster with the Variational Iteration method compared to the Adomian decomposition method. Also, using graphical simulation, this study found the output Y(t) is closer to the exact solution with α=0.4 and α=0.9. In conclusion, this study successfully solved natural growth with memory effect in economics and decided the best model between FDE, namely Adomian decomposition and Variational iterative methods using numerical analysis.

A possible modification of groundwater flow equation using coordinate transformations

2014 ◽  
Vol 15 (2) ◽  
pp. 278-287 ◽  
Author(s):  
Abdon Atangana ◽  
Ernestine Alabaraoye
Keyword(s):  
Groundwater Flow ◽  
Prolate Spheroid ◽  
Flow Equation ◽  
Time Space ◽  
Adomian Decomposition ◽  
Iteration Methods ◽  
Groundwater Flow Equation ◽  
Factor Α ◽  
Modified Equation ◽  
Good Agreement

We described a groundwater model with prolate spheroid coordinates, and introduced a new parameter, namely τ the silhouette influence of the geometric under which the water flows. At first, we supposed that the silhouette influence approaches zero; under this assumption, the modified equation collapsed to the ordinary groundwater flow equation. We proposed an analytical solution to the standard version of groundwater as a function of time, space and uncertainty factor α. Our proposed solution was in good agreement with experimental data. We presented a good approximation to the exponential integral. We obtained an asymptotic special solution to the modified equation by means of the Adomian decomposition and variational iteration methods.

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