A general approach to specific second order ordinary differential equations using homotopy perturbation method

2008 ◽  
Vol 372 (30) ◽  
pp. 4973-4976 ◽  
Author(s):  
Arif Rafiq ◽  
Munshoor Ahmed ◽  
Sifat Hussain
Keyword(s):  
Differential Equations ◽  
Perturbation Method ◽  
Ordinary Differential Equations ◽  
Homotopy Perturbation Method ◽  
Second Order ◽  
Homotopy Perturbation

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.

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

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 Least Square Homotopy Perturbation Method for Ordinary Differential Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Mubashir Qayyum ◽  
Imbsat Oscar
Keyword(s):  
Differential Equations ◽  
Perturbation Method ◽  
Ordinary Differential Equations ◽  
Homotopy Perturbation Method ◽  
Least Square ◽  
Literature Analysis ◽  
Science And Engineering ◽  
Homotopy Perturbation ◽  
Seventh Order ◽  
Linear And Nonlinear

In this study, a new modification of the homotopy perturbation method (HPM) is introduced for various order boundary value problems (BVPs). In this modification, HPM is hybrid with least square optimizer and named as the least square homotopy perturbation method (LSHPM). The proposed scheme is tested against various linear and nonlinear BVPs (second to seventh order DEs). Validity of the obtained solutions is confirmed by finding absolute errors. To analyze the efficiency of the proposed scheme, tested problems have also been solved through HPM and results are compared with LSHPM. Furthermore, obtained results are also compared with other numerical schemes available in literature. Analysis reveals that LSHPM is a consistent and effective scheme which can be used for more complex BVPs in science and engineering.

scholarly journals Semi-Analytical Resolution of a Squeezing Unsteady Nanofluid Flow Between Two Parallel Plates Using Homotopy Perturbation Method (HPM)

2021 ◽  
Vol 16 ◽  
pp. 1-13 ◽  
Author(s):  
A. El Harfouf ◽  
A. Wakif ◽  
S. Hayani Mounir
Keyword(s):  
Differential Equations ◽  
Perturbation Method ◽  
Ordinary Differential Equations ◽  
Homotopy Perturbation Method ◽  
Skin Friction Coefficient ◽  
Heat Transfer Analysis ◽  
Squeezing Flow ◽  
Nonlinear Ordinary Differential Equations ◽  
Parallel Plates ◽  
Homotopy Perturbation

In this current work, the heat transfer analysis for the unsteady squeezing flow of a viscous nanofluid between two parallel plates 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 (HPM). The results found in this peper are verified by comparing it with the results obtained using the numerical method RK4, The results obtained are agree with this numerical solution. 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.

scholarly journals Quantum homotopy perturbation method for nonlinear dissipative ordinary differential equations

2021 ◽  
Author(s):  
Cheng Xue ◽  
Wu Yu-Chun ◽  
GuoPing Guo
Keyword(s):  
Differential Equations ◽  
Perturbation Method ◽  
Ordinary Differential Equations ◽  
Homotopy Perturbation Method ◽  
Quantum Algorithms ◽  
Nonlinear Differential Equations ◽  
Success Probability ◽  
Nonlinear Odes ◽  
Homotopy Perturbation ◽  
Linear Odes

Abstract While quantum computing provides an exponential advantage in solving linear differential equations, there are relatively few quantum algorithms for solving nonlinear differential equations. In our work, based on the homotopy perturbation method, we propose a quantum algorithm for solving n-dimensional nonlinear dissipative ordinary differential equations (ODEs). Our algorithm first converts the original nonlinear ODEs into other nonlinear ODEs which can be embedded into finite-dimensional linear ODEs. Then we solve the embedded linear ODEs with quantum linear ODEs algorithm and obtain a state ε-close to the normalized exact solution of the original nonlinear ODEs with success probability Ω(1). The complexity of our algorithm is O(gηTpoly(log(nT/ε))), where η, g measure the decay of the solution. Our algorithm provides exponential improvement over the best classical algorithms or previous quantum algorithms in n or ε.

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