The Homotopy Perturbation Method for Solving Singular Initial Value Problems

2009 ◽  
Vol 10 (2) ◽  
Author(s):  
A. Yildirim ◽  
D. Agirseven
Keyword(s):  
Perturbation Method ◽  
Initial Value Problems ◽  
Homotopy Perturbation Method ◽  
Initial Value ◽  
Homotopy Perturbation

Homotopy Perturbation Method for a Class of Nonlinear Singular System of Initial Value Problems

2020 ◽  
Vol 12 (1) ◽  
pp. 60-64
Author(s):  
Priti Pathak ◽  
Amit K. Barnwal
Keyword(s):  
Perturbation Method ◽  
Convergence Analysis ◽  
Initial Value Problems ◽  
Homotopy Perturbation Method ◽  
Singular System ◽  
Initial Value ◽  
Recursive Scheme ◽  
Homotopy Perturbation ◽  
Nonlinear Singular System

In this paper, a method based on homotopy perturbation method is used to establish the recursive scheme for the solution of nonlinear singular system of initial value problems. The convergence analysis of the proposed method is also shown. The accuracy and efficiency of the proposed method are demonstrated through various examples.

scholarly journals A local fractional homotopy perturbation method for solving the local fractional Korteweg-de Vries equations with non-homogeneous term

2019 ◽  
Vol 23 (3 Part A) ◽  
pp. 1495-1501 ◽  
Author(s):  
Yong-Ju Yang ◽  
Shun-Qin Wang
Keyword(s):  
Perturbation Method ◽  
Initial Value Problems ◽  
Homotopy Perturbation Method ◽  
Validity And Reliability ◽  
Initial Value ◽  
Homotopy Perturbation ◽  
De Vries

In this paper, a local fractional homotopy perturbation method is presented to solve the boundary and initial value problems of the local fractional Korteweg-de Vries equations with non-homogeneous term. In order to demonstrate the validity and reliability of the method, two types of the Korteweg-de Vries equations with non-homogeneous term are proposed.

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. 

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