scholarly journals Application of the Homotopy Perturbation Method to Nonlinear Heat Conduction and Fractional Van der Pol Damped Nonlinear Oscillator

2014 ◽  
Vol 05 (06) ◽  
pp. 852-861 ◽  
Author(s):  
T. A. Nofel
Keyword(s):  
Heat Conduction ◽  
Perturbation Method ◽  
Nonlinear Oscillator ◽  
Homotopy Perturbation Method ◽  
Nonlinear Heat Conduction ◽  
Van Der Pol ◽  
Homotopy Perturbation

scholarly journals Solution of the inverse heat conduction problem with Neumann boundary condition by using the homotopy perturbation method

2013 ◽  
Vol 17 (3) ◽  
pp. 643-650 ◽  
Author(s):  
Edyta Hetmaniok ◽  
Iwona Nowak ◽  
Damian Slota ◽  
Roman Witula ◽  
Adam Zielonka
Keyword(s):  
Boundary Condition ◽  
Heat Conduction ◽  
Perturbation Method ◽  
Neumann Boundary Condition ◽  
Homotopy Perturbation Method ◽  
Heat Conduction Problem ◽  
Neumann Boundary ◽  
Inverse Heat Conduction Problem ◽  
Inverse Heat Conduction ◽  
Homotopy Perturbation

In the paper a solution of the inverse heat conduction problem with the Neumann boundary condition is presented. For finding this solution the homotopy perturbation method is applied. Investigated problem consists in calculation of the temperature distribution in considered domain, as well as in reconstruction of the functions describing the temperature and the heat flux on the boundary, in case when the temperature measurements in some points of the domain are known. An example confirming usefulness of the homotopy perturbation method for solving problems of this kind are also included.

scholarly journals An Effective Solution of the Cube-Root Truly Nonlinear Oscillator: Extended Iteration Procedure

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
B. M. Ikramul Haque ◽  
M. M. Ayub Hossain
Keyword(s):  
Perturbation Method ◽  
Iteration Method ◽  
Harmonic Balance ◽  
Nonlinear Oscillator ◽  
Homotopy Perturbation Method ◽  
Harmonic Balance Method ◽  
Percentage Error ◽  
Cube Root ◽  
Homotopy Perturbation ◽  
Approximate Frequency

The cube-root truly nonlinear oscillator and the inverse cube-root truly nonlinear oscillator are the most meaningful and classical nonlinear ordinary differential equations on behalf of its various applications in science and engineering. Especially, the oscillators are used widely in the study of elastic force, structural dynamics, and elliptic curve cryptography. In this paper, we have applied modified Mickens extended iteration method to solve the cube-root truly nonlinear oscillator, the inverse cube-root truly nonlinear oscillator, and the equation of pendulum. Comparison is made among iteration method, harmonic balance method, He’s amplitude-frequency formulation, He’s homotopy perturbation method, improved harmonic balance method, and homotopy perturbation method. After comparison, we analyze that modified Mickens extended iteration method is more accurate, effective, easy, and straightforward. Also, the comparison of the obtained analytical solutions with the numerical results represented an extraordinary accuracy. The percentage error for the fourth approximate frequency of cube-root truly nonlinear oscillator is 0.006 and the percentage error for the fourth approximate frequency of inverse cube-root truly nonlinear oscillator is 0.12.

Sign in / Sign up

Export Citation Format

Share Document