New iterative methods for solving nonlinear equation by using homotopy perturbation method

2012 ◽  
Vol 219 (8) ◽  
pp. 3565-3574 ◽  
Author(s):  
Muhammad Aslam Noor ◽  
Waseem Asghar Khan
Keyword(s):  
Nonlinear Equation ◽  
Perturbation Method ◽  
Iterative Methods ◽  
Homotopy Perturbation Method ◽  
Homotopy Perturbation

scholarly journals Study on Space-Time Fractional Nonlinear Biological Equation in Radial Symmetry

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Yanqin Liu
Keyword(s):  
Nonlinear Equation ◽  
Fractional Derivative ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Approximate Solutions ◽  
Radial Symmetry ◽  
Space Time ◽  
Homotopy Perturbation ◽  
Initial Stage

We consider the initial stage of space-time fractional generalized biological equation in radial symmetry. Dimensionless multiorder fractional nonlinear equation was first given, and approximate solutions were derived in the form of series using the homotopy perturbation method with a new modification. And the influence of fractional derivative is also discussed.

Free Oscillations of a Nonlinear Oscillator with an Exponential Non-Viscous Damping

2015 ◽  
Vol 801 ◽  
pp. 38-42 ◽  
Author(s):  
Remus Daniel Ene ◽  
Vasile Marinca ◽  
Bogdan Marinca
Keyword(s):  
Nonlinear Equation ◽  
Perturbation Method ◽  
Periodic Solutions ◽  
Nonlinear Oscillator ◽  
Homotopy Perturbation Method ◽  
Nonlinear Oscillations ◽  
Initial Conditions ◽  
Viscous Damping ◽  
Free Oscillations ◽  
Homotopy Perturbation

This paper deals with the nonlinear oscillations of an exponential non-viscous damping oscillator. An analytic technique, namely Optimal Homotopy Perturbation Method (OHPM) is employed to propose an analytic approach to solve nonlinear oscillations. Our procedure proved to very effective and accurate and did not require a small or large parameters in the nonlinear equation or in the initial conditions. An excellent agreement of the approximate frequencies and periodic solutions with the numerical ones has been demonstrated.

On Spectral-Homotopy Perturbation Method Solution of Nonlinear Differential Equations in Bounded Domains

2013 ◽  
Vol 1 (1) ◽  
pp. 25-37
Author(s):  
Ahmed A. Khidir
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Nonlinear Boundary ◽  
Nonlinear Differential Equations ◽  
Iteration Algorithm ◽  
Test Problems ◽  
Nonlinear Boundary Value Problems ◽  
Homotopy Perturbation ◽  
Spectral Technique ◽  
Homotopy Analysis

In this study, a combination of the hybrid Chebyshev spectral technique and the homotopy perturbation method is used to construct an iteration algorithm for solving nonlinear boundary value problems. Test problems are solved in order to demonstrate the efficiency, accuracy and reliability of the new technique and comparisons are made between the obtained results and exact solutions. The results demonstrate that the new spectral homotopy perturbation method is more efficient and converges faster than the standard homotopy analysis method. The methodology presented in the work is useful for solving the BVPs consisting of more than one differential equation in bounded domains. 

A new modification of the homotopy perturbation method

2021 ◽  
pp. 095745652199987
Author(s):  
Magaji Yunbunga Adamu ◽  
Peter Ogenyi
Keyword(s):  
Comparative Analysis ◽  
Error Analysis ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Nonlinear Oscillators ◽  
Absolute Error ◽  
New Method ◽  
Optimal Analysis ◽  
Homotopy Perturbation ◽  
Accuracy And Precision

This study proposes a new modification of the homotopy perturbation method. A new parameter alpha is introduced into the homotopy equation in order to improve the results and accuracy. An optimal analysis identifies the parameter alpha, aimed at improving the solutions. A comparative analysis of the proposed method reveals that the new method presents results with higher degree of accuracy and precision than the classic homotopy perturbation method. Absolute error analysis shows the convenience of the proposed method, providing much smaller errors. Two examples are presented: Duffing and Van der pol’s nonlinear oscillators to demonstrate the efficiency, accuracy, and applicability of the new method.

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