Approximate Solution of the Electrostatic Nano‐Cantilever Model via Optimal Perturbation Iteration Method

2021 ◽  
Author(s):  
Waleed Adel ◽  
Sinan Deniz
Keyword(s):  
Approximate Solution ◽  
Iteration Method ◽  
Optimal Perturbation

scholarly journals The Approximate Solution of Fractional Fredholm Integrodifferential Equations by Variational Iteration and Homotopy Perturbation Methods

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Abdelouahab Kadem ◽  
Adem Kilicman
Keyword(s):  
Approximate Solution ◽  
Perturbation Method ◽  
Iteration Method ◽  
Homotopy Perturbation Method ◽  
Perturbation Methods ◽  
Variational Iteration Method ◽  
Integrodifferential Equations ◽  
Variational Iteration ◽  
Homotopy Perturbation ◽  
Constant Coefficients

Variational iteration method and homotopy perturbation method are used to solve the fractional Fredholm integrodifferential equations with constant coefficients. The obtained results indicate that the method is efficient and also accurate.

An optimal iteration method with application to the Thomas-Fermi equation

Open Physics ◽  
2011 ◽  
Vol 9 (3) ◽  
Author(s):  
Vasile Marinca ◽  
Nicolae Herişanu
Keyword(s):  
Approximate Solution ◽  
Approximate Method ◽  
Iteration Method ◽  
Nonlinear Problems ◽  
Analytical Approximate Solution ◽  
Thomas Fermi ◽  
Strongly Nonlinear ◽  
Good Agreement

AbstractThe aim of this paper is to introduce a new approximate method, namely the Optimal Parametric Iteration Method (OPIM) to provide an analytical approximate solution to Thomas-Fermi equation. This new iteration approach provides us with a convenient way to optimally control the convergence of the approximate solution. A good agreement between the obtained solution and some well-known results has been demonstrated. The proposed technique can be easily applied to handle other strongly nonlinear problems.

scholarly journals Asymptotic Solution for a Class of Epidemic Contagion Ecological Nonlinear Systems

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Yi-Hu Feng ◽  
Lei Hou
Keyword(s):  
Approximate Solution ◽  
Nonlinear System ◽  
Nonlinear Systems ◽  
Asymptotic Solution ◽  
Iteration Method ◽  
Ecological Model ◽  
Virus Transmission ◽  
Practical Application ◽  
Generalized Variation ◽  
Variation Iteration Method

In this paper, a class of systems for epidemic contagion is considered. An epidemic virus ecological model is described. Using the generalized variation iteration method, the corresponding approximate solution to the nonlinear system is obtained and the method for this approximate solution is pointed out. The accuracy of approximate solution is discussed, and it can control the epidemic virus transmission by using the parameters of the system. Thus, it has the value for practical application.

scholarly journals Variational Iteration Method for Solving the Generalized Degasperis-Procesi Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Qian Lijuan ◽  
Tian Lixin ◽  
Ma Kaiping
Keyword(s):  
Approximate Solution ◽  
Exact Solutions ◽  
Lagrange Multiplier ◽  
Iteration Method ◽  
Initial Approximation ◽  
Variational Iteration Method ◽  
Original Equation ◽  
Variational Iteration

We introduce the variational iteration method for solving the generalized Degasperis-Procesi equation. Firstly, according to the variational iteration, the Lagrange multiplier is found after making the correction functional. Furthermore, several approximations ofun+1(x,t)which is converged tou(x,t)are obtained, and the exact solutions of Degasperis-Procesi equation will be obtained by using the traditional variational iteration method with a suitable initial approximationu0(x,t). Finally, after giving the perturbation item, the approximate solution for original equation will be expressed specifically.

scholarly journals Approximate Solution of Linear Fuzzy Initial Value Problems Using Modified Variaional Iteration Method

2021 ◽  
Vol 24 (4) ◽  
pp. 32-39
Author(s):  
Hussein M. Sagban ◽  
◽  
Fadhel S. Fadhel ◽  
Keyword(s):  
Approximate Solution ◽  
Rate Of Convergence ◽  
Initial Value Problem ◽  
Iteration Method ◽  
Initial Value Problems ◽  
Initial Conditions ◽  
Variational Iteration Method ◽  
Initial Value ◽  
Variational Iteration ◽  
Modified Variational Iteration Method

The main objective of this paper is to solve fuzzy initial value problems, in which the fuzziness occurs in the initial conditions. The proposed approach, namely the modified variational iteration method, will be used to find the solution of fuzzy initial value problem approximately and to increase the rate of convergence of the variational iteration method. From the obtained results, as it is expected, the approximate results of the proposed method are more accurate than those results obtained without using the modified variational iteration method.

scholarly journals Application of the Variational Iteration Method to Strongly Nonlinear -Difference Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
Hsuan-Ku Liu
Keyword(s):  
Approximate Solution ◽  
Time Scales ◽  
Difference Equations ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Numerical Results ◽  
Series Solutions ◽  
Nonlinear Difference Equations ◽  
Strongly Nonlinear ◽  
Variational Iteration

The theory of approximate solution lacks development in the area of nonlinear -difference equations. One of the difficulties in developing a theory of series solutions for the homogeneous equations on time scales is that formulas for multiplication of two -polynomials are not easily found. In this paper, the formula for the multiplication of two -polynomials is presented. By applying the obtained results, we extend the use of the variational iteration method to nonlinear -difference equations. The numerical results reveal that the proposed method is very effective and can be applied to other nonlinear -difference equations.

Sign in / Sign up

Export Citation Format

Share Document