scholarly journals An analytical approximation to the solution of a wave equation by a variational iteration method

2008 ◽  
Vol 21 (8) ◽  
pp. 780-785 ◽  
Author(s):  
J. Biazar ◽  
H. Ghazvini
Keyword(s):  
Wave Equation ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Analytical Approximation ◽  
Variational Iteration

scholarly journals Solution of Wave Equation in Radial Form by VIM

2012 ◽  
Vol 2012 ◽  
pp. 1-3
Author(s):  
Hossein Aminikhah
Keyword(s):  
Wave Equation ◽  
Boundary Conditions ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Analytic Approximation ◽  
Variational Iteration ◽  
Initial And Boundary Conditions

An analytic approximation to the solution of wave equation is studied. Wave equation is in radial form with indicated initial and boundary conditions, by variational iteration method it has been used to derive this approximation and some examples are presented to show the simplicity and efficiency of the method.

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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