scholarly journals Modified nonlinearities distribution Homotopy Perturbation method as a tool to find power series solutions to ordinary differential equations

Nova Scientia ◽  
2014 ◽  
Vol 6 (12) ◽  
pp. 13 ◽  
Author(s):  
Umberto Filobello-Nino ◽  
Héctor Vázquez-Leal ◽  
Yasir Khan ◽  
D. Pereyra-Díaz ◽  
A. Pérez-Sesma ◽  
...  
Keyword(s):  
Power Series ◽  
Differential Equations ◽  
Perturbation Method ◽  
Ordinary Differential Equations ◽  
Homotopy Perturbation Method ◽  
Initial Conditions ◽  
Series Solutions ◽  
Homotopy Perturbation ◽  
Polynomial Coefficients ◽  
Power Series Solutions

In this article, modified non-linearities distribution homotopy perturbation method (MNDHPM) is used in order to find power series solutions to ordinary differential equations with initial conditions, both linear and nonlinear. We will see that the method is particularly relevant in some cases of equations with non-polynomial coefficients and inhomogeneous non-polynomial terms

Application of He’s Homotopy Perturbation Method to Stiff Systems of Ordinary Differential Equations

2008 ◽  
Vol 63 (1-2) ◽  
pp. 19-23 ◽  
Author(s):  
Mohammad Taghi Darvishi ◽  
Farzad Khani
Keyword(s):  
Analytical Solution ◽  
Differential Equations ◽  
Perturbation Method ◽  
Ordinary Differential Equations ◽  
Homotopy Perturbation Method ◽  
Nonlinear Ordinary Differential Equations ◽  
Stiff Systems ◽  
Homotopy Perturbation ◽  
Linear And Nonlinear

We propose He’s homotopy perturbation method (HPM) to solve stiff systems of ordinary differential equations. This method is very simple to be implemented. HPM is employed to compute an approximation or analytical solution of the stiff systems of linear and nonlinear ordinary differential equations.

Heat Transfer Analysis on Squeezing Unsteady MHD Nanofluid Flow Between Two Parallel Plates Considering Thermal Radiation, Magnetic and Viscous Dissipations Effects a Solution by Using Homotopy Perturbation Method

2020 ◽  
Vol 18 (2) ◽  
pp. 113-121
Author(s):  
A. El Harfouf ◽  
A. Wakif ◽  
S. Hayani Mounir
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Perturbation Method ◽  
Ordinary Differential Equations ◽  
Homotopy Perturbation Method ◽  
Heat Transfer Analysis ◽  
Nonlinear Ordinary Differential Equations ◽  
Parallel Plates ◽  
Homotopy Perturbation

In this current work, the heat transfer analysis for the unsteady squeezing magnetohydrodynamic flow of a viscous nanofluid between two parallel plates in the presence of thermal radiation, viscous and magnetic dissipations impacts, considering Fourier heat flux model have been explored. The partial differential equations representing flow model are reduced to nonlinear ordinary differential equations by introducing a similarity transformation. The dimensionless and nonlinear ordinary differential equations of the velocity and temperatures functions obtained are solved by employing the homotopy perturbation method. The effects of different parameters on the velocity and temperature profiles are examined graphically, and numerical calculations for the skin friction coefficient and local Nusselt number are tabulated. It is found an excellent agreement in the comparative study with literature results. This present numerical exploration has great relevance, consequently a better understanding of the squeezing flow phenomena in the hydraulic lifts, power transmission, nano gastric tubes, reactor fluidization areas.

scholarly journals Rational Biparameter Homotopy Perturbation Method and Laplace-Padé Coupled Version

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Hector Vazquez-Leal ◽  
Arturo Sarmiento-Reyes ◽  
Yasir Khan ◽  
Uriel Filobello-Nino ◽  
Alejandro Diaz-Sanchez
Keyword(s):  
Power Series ◽  
Differential Equations ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Nonlinear Differential Equations ◽  
Approximate Solutions ◽  
Van Der Pol Oscillator ◽  
Van Der Pol ◽  
Homotopy Perturbation ◽  
Physical Phenomena

The fact that most of the physical phenomena are modelled by nonlinear differential equations underlines the importance of having reliable methods for solving them. This work presents the rational biparameter homotopy perturbation method (RBHPM) as a novel tool with the potential to find approximate solutions for nonlinear differential equations. The method generates the solutions in the form of a quotient of two power series of different homotopy parameters. Besides, in order to improve accuracy, we propose the Laplace-Padé rational biparameter homotopy perturbation method (LPRBHPM), when the solution is expressed as the quotient of two truncated power series. The usage of the method is illustrated with two case studies. On one side, a Ricatti nonlinear differential equation is solved and a comparison with the homotopy perturbation method (HPM) is presented. On the other side, a nonforced Van der Pol Oscillator is analysed and we compare results obtained with RBHPM, LPRBHPM, and HPM in order to conclude that the LPRBHPM and RBHPM methods generate the most accurate approximated solutions.

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