scholarly journals Variational Iteration Method and Differential Transformation Method for Solving the SEIR Epidemic Model

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
A. Harir ◽  
S. Melliani ◽  
H. El Harfi ◽  
L. S. Chadli
Keyword(s):  
Mathematical Model ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Transformation Method ◽  
Differential Transformation Method ◽  
Nonlinear Ordinary Differential Equations ◽  
Nonlinear Odes ◽  
Differential Transformation ◽  
Variational Iteration ◽  
The Mathematical Model

The aim of the present study is to analyze and find a solution for the model of nonlinear ordinary differential equations (ODEs) describing the so-called coronavirus (COVID-19), a deadly and most parlous virus. The mathematical model based on four nonlinear ODEs is presented, and the corresponding numerical results are studied by applying the variational iteration method (VIM) and differential transformation method (DTM).

scholarly journals The Solution of a Mathematical Model for Dengue Fever Transmission Using Differential Transformation Method

2019 ◽  
pp. 82-87
Author(s):  
Felix Yakubu Eguda ◽  
Andrawus James ◽  
Sunday Babuba
Keyword(s):  
Mathematical Model ◽  
Dengue Fever ◽  
Transformation Method ◽  
Vital Role ◽  
Differential Transformation Method ◽  
Linear Ordinary Differential Equations ◽  
Differential Transformation ◽  
Long Term Behavior ◽  
The Mathematical Model

Differential Transformation Method (DTM) is a very effective tool for solving linear and non-linear ordinary differential equations. This paper uses DTM to solve the mathematical model for the dynamics of Dengue fever in a population. The graphical profiles for human population are obtained using Maple software. The solution profiles give the long term behavior of Dengue fever model which shows that treatment plays a vital role in reducing the disease burden in a population.

The variational iteration method for solving linear and nonlinear ODEs and scientific models with variable coefficients

2014 ◽  
Vol 4 (1) ◽  
Author(s):  
Abdul-Majid Wazwaz
Keyword(s):  
Porous Medium ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Variable Coefficients ◽  
Scientific Models ◽  
Nonlinear Ordinary Differential Equations ◽  
Nonlinear Odes ◽  
Variational Iteration ◽  
Hybrid Selection ◽  
Linear And Nonlinear

AbstractWe apply the variational iteration method (VIM) for solving linear and nonlinear ordinary differential equations with variable coefficients. We use distinct Lagrange multiplier for each order of ODE. We emphasize the power of the method by testing a variety of models with distinct orders and variable coefficients. Scientific models, namely, the hybrid selection model, the Thomas-Fermi equation, the Kidder equation of the Unsteady flow of gas through a porous medium, and the Riccati equation, are studied as well.

scholarly journals Mathematical Model and Solution for Fingering Phenomenon in Double Phase Flow through Homogeneous Porous Media

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Piyush R. Mistry ◽  
Vikas H. Pradhan ◽  
Khyati R. Desai
Keyword(s):  
Mathematical Model ◽  
Porous Media ◽  
Iteration Method ◽  
Physical Phenomenon ◽  
Nonlinear Partial Differential Equation ◽  
Variational Iteration Method ◽  
Phase Flow ◽  
Variational Iteration ◽  
Double Phase ◽  
Flow Through

The present paper analytically discusses the phenomenon of fingering in double phase flow through homogenous porous media by using variational iteration method. Fingering phenomenon is a physical phenomenon which occurs when a fluid contained in a porous medium is displaced by another of lesser viscosity which frequently occurred in problems of petroleum technology. In the current investigation a mathematical model is presented for the fingering phenomenon under certain simplified assumptions. An approximate analytical solution of the governing nonlinear partial differential equation is obtained using variational iteration method with the use of Mathematica software.

Lateral-Torsional Stability of Rectangular Prismatic Beams Using Some Analytical Approximation Techniques

2020 ◽  
Vol 20 (02) ◽  
pp. 2050027
Author(s):  
Ahmet Yücesoy ◽  
Safa Bozkurt Coşkun
Keyword(s):  
Iteration Method ◽  
Adomian Decomposition Method ◽  
Variational Iteration Method ◽  
Transformation Method ◽  
Single Equation ◽  
Analytical Approximation ◽  
Governing Equations ◽  
Approximation Techniques ◽  
Variational Iteration ◽  
Adomian Decomposition

The paper presents simple computational algorithms for analyzing the lateral-torsional buckling of prismatic beams with rectangular cross-sections under bending action due to uniform and nonuniform loads by the Adomian decomposition method (ADM) and variational iteration method (VIM). Unlike the numerical techniques that lead to a discretization process, the proposed method allows us to derive the solution in terms of an analytical function for the problem considered. Although the governing equations of the problem appear as a system of two coupled variable coefficient ordinary differential equations, they reduce to a single equation for rectangular beams. The buckling loads for different loading conditions are computed, with the results for the simple beam compared with previous available results by the differential transformation method (DTM), variational iteration method (VIM) and finite element method (FEM) based on coupled governing equations. The results clearly show the efficiency and advantage of the present technique over those based on the coupled governing equations using the DTM and VIM in view of the number of terms required to obtain the convergent solution.

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