scholarly journals SOLUTION OF AN INTEGRO-DIFFERENTIAL EQUATION ARISING IN OSCILLATING MAGNETIC FIELDS USING HE'S HOMOTOPY PERTURBATION METHOD

2008 ◽  
Vol 78 ◽  
pp. 361-376 ◽  
Author(s):  
Mehdi Dehghan ◽  
Fatemeh Shakeri
Keyword(s):  
Differential Equation ◽  
Magnetic Fields ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Integro Differential Equation ◽  
Homotopy Perturbation

scholarly journals A Reliable Treatment of Homotopy Perturbation Method for Solving the Nonlinear Klein-Gordon Equation of Arbitrary (Fractional) Orders

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
A. M. A. El-Sayed ◽  
A. Elsaid ◽  
D. Hammad
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Gordon Equation ◽  
Numerical Examples ◽  
Homotopy Perturbation ◽  
Klein Gordon ◽  
Fractional Orders ◽  
Klein Gordon Equation

The reliable treatment of homotopy perturbation method (HPM) is applied to solve the Klein-Gordon partial differential equation of arbitrary (fractional) orders. This algorithm overcomes the difficulty that arises in calculating complicated integrals when solving nonlinear equations. Some numerical examples are presented to illustrate the efficiency of this technique.

Nonlinear Vibration Analysis of Functionally Graded Nanobeam Using Homotopy Perturbation Method

2016 ◽  
Vol 9 (1) ◽  
pp. 144-156 ◽  
Author(s):  
Majid Ghadiri ◽  
Mohsen Safi
Keyword(s):  
Differential Equation ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Nonlinear Partial Differential Equation ◽  
Beam Theory ◽  
Nonlocal Elasticity Theory ◽  
Functionally Graded ◽  
Simply Supported ◽  
Homotopy Perturbation ◽  
Functionally Graded Nanobeam

AbstractIn this paper, He's homotopy perturbation method is utilized to obtain the analytical solution for the nonlinear natural frequency of functionally graded nanobeam. The functionally graded nanobeam is modeled using the Eringen's nonlocal elasticity theory based on Euler-Bernoulli beam theory with von Karman nonlinearity relation. The boundary conditions of problem are considered with both sides simply supported and simply supported-clamped. The Galerkin's method is utilized to decrease the nonlinear partial differential equation to a nonlinear second-order ordinary differential equation. Based on numerical results, homotopy perturbation method convergence is illustrated. According to obtained results, it is seen that the second term of the homotopy perturbation method gives extremely precise solution.

Solution for Celebrated Blasius Problem Using Homotopy Perturbation Method

2020 ◽  
Vol 12 (2) ◽  
pp. 284-287
Author(s):  
Monika Rani ◽  
Vikramjeet Singh ◽  
Rakesh Goyal
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Perturbation Method ◽  
High Speed ◽  
Homotopy Perturbation Method ◽  
Initial Slope ◽  
Moving Wall ◽  
Homotopy Perturbation ◽  
Blasius Problem ◽  
Blasius Equation

In this manuscript, we have analyzed Celebrated Blasius boundary problem with moving wall or high speed 2D laminar viscous flow over gasifying flat plate. To find the way out of this nonlinear differential equation, a version of semi-analytical homotopy perturbation method has been applied. It has been observed that the precision of the solution would be achieved with increasing approximations. On comparison with literature, our solution has been proven highly accurate and valid with faster rate of convergence. It has been revealed that the second order approximate solution of Blasius equation in terms of initial slope is obtained as 0.33315 reducing the error by 0.32%.

Application of the enhanced homotopy perturbation method to solve the fractional-order Bagley–Torvik differential equation

2009 ◽  
Vol T136 ◽  
pp. 014032 ◽  
Author(s):  
M Zolfaghari ◽  
R Ghaderi ◽  
A SheikholEslami ◽  
A Ranjbar ◽  
S H Hosseinnia ◽  
...  
Keyword(s):  
Differential Equation ◽  
Perturbation Method ◽  
Fractional Order ◽  
Homotopy Perturbation Method ◽  
Homotopy Perturbation
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