Application of homotopy perturbation and variational iteration methods for nonlinear imprecise prey–predator model with stability analysis

2021 ◽  
Author(s):  
T. Vijayalakshmi ◽  
R. Senthamarai
Keyword(s):  
Stability Analysis ◽  
Variational Iteration ◽  
Homotopy Perturbation ◽  
Iteration Methods ◽  
Predator Model

scholarly journals Application of Homotopy Perturbation and Variational Iteration Methods for Fredholm Integrodifferential Equation of Fractional Order

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Asma Ali Elbeleze ◽  
Adem Kiliçman ◽  
Bachok M. Taib
Keyword(s):  
Numerical Methods ◽  
Boundary Conditions ◽  
Fractional Order ◽  
Integrodifferential Equation ◽  
Fractional Derivatives ◽  
Initial Boundary ◽  
Variational Iteration ◽  
Homotopy Perturbation ◽  
Iteration Methods

This paper presents the application of homotopy perturbation and variational iteration methods as numerical methods for Fredholm integrodifferential equation of fractional order with initial-boundary conditions. The fractional derivatives are described in Caputo sense. Some illustrative examples are presented.

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.

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