scholarly journals Some closed-form solutions for buckling of straight beams with varying cross-section by Variational Iteration Method with Generalized Lagrange Multipliers

2018 ◽  
Vol 10 (3) ◽  
pp. 159-175
Author(s):  
Ugurcan Eroglu ◽  
Ekrem Tüfekci
Keyword(s):  
Closed Form ◽  
Cross Section ◽  
Lagrange Multipliers ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Closed Form Solutions ◽  
Variational Iteration

scholarly journals Variational Iteration Method for the Solution of Differential Equation of Motion of the Mathematical Pendulum and Duffing-Harmonic Oscillator

2019 ◽  
pp. 101-109
Author(s):  
Muhammad Munib Khan
Keyword(s):  
Differential Equation ◽  
Harmonic Oscillator ◽  
Lagrange Multipliers ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Equation Of Motion ◽  
Mathematical Pendulum ◽  
Variational Iteration ◽  
Common Problems

In this work, the differential equation of motion of the undamped mathematical pendulum and Duffing-harmonic oscillator are discussed by using the variational iteration method. Additionally, common problems of pendulum are classified and Lagrange multipliers are obtained for each type of problem. Examples are given for illustration.

scholarly journals Variational Iteration Method for Singular Perturbation Initial Value Problems with Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Yongxiang Zhao ◽  
Aiguo Xiao ◽  
Li Li ◽  
Chengjian Zhang
Keyword(s):  
Singular Perturbation ◽  
Lagrange Multipliers ◽  
Iteration Method ◽  
Initial Value Problems ◽  
Variational Iteration Method ◽  
Variational Theory ◽  
Initial Value ◽  
Numerical Examples ◽  
Variational Iteration ◽  
Convergence Results

The variational iteration method (VIM) is applied to solve singular perturbation initial value problems with delays (SPIVPDs). Some convergence results of VIM for solving SPIVPDs are given. The obtained sequence of iterates is based on the use of general Lagrange multipliers; the multipliers in the functionals can be identified by the variational theory. Moreover, the numerical examples show the efficiency of the method.

scholarly journals The extended variational iteration method for local fractional differential equation

2021 ◽  
pp. 54-54
Author(s):  
Yong-Ju Yang
Keyword(s):  
Differential Equation ◽  
Fractional Derivative ◽  
Lagrange Multipliers ◽  
Iteration Method ◽  
Sufficient Conditions ◽  
Variational Iteration Method ◽  
Variational Iteration ◽  
Sufficient Conditions For Convergence ◽  
Fractional Differential ◽  
First Time

An extended variational iteration method within the local fractional derivative is introduced for the first time., where two Lagrange multipliers are adopted. Moreover, the sufficient conditions for convergence of the new variational iteration method are also established..

scholarly journals Variational Iteration Method for the Solution of Differential Equation of Motion of the Mathematical Pendulum and Duffing-Harmonic Oscillator

2019 ◽  
pp. 101-109
Author(s):  
Muhammad Munib Khan
Keyword(s):  
Differential Equation ◽  
Harmonic Oscillator ◽  
Lagrange Multipliers ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Equation Of Motion ◽  
Mathematical Pendulum ◽  
Variational Iteration ◽  
Common Problems

In this work, the differential equation of motion of the undamped mathematical pendulum and Duffing-harmonic oscillator are discussed by using the variational iteration method. Additionally, common problems of pendulum are classified and Lagrange multipliers are obtained for each type of problem. Examples are given for illustration.

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