Variational homotopy perturbation method of quadratic integral equations

2017 ◽  
Vol 11 ◽  
pp. 623-635
Author(s):  
Hind Al-badrani ◽  
F. A. Hendi ◽  
Wafa Shammakh
Keyword(s):  
Perturbation Method ◽  
Integral Equations ◽  
Homotopy Perturbation Method ◽  
Homotopy Perturbation ◽  
Quadratic Integral ◽  
Quadratic Integral Equations

scholarly journals Numerical Solutions of a Quadratic Integral Equations by Using Variational Iteration and Homotopy Perturbation Methods

2017 ◽  
Vol 9 (2) ◽  
pp. 134
Author(s):  
Hind Al-badrani ◽  
F. A. Hendi ◽  
Wafa Shammakh
Keyword(s):  
Integral Equations ◽  
Homotopy Perturbation Method ◽  
Numerical Solutions ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Convergent Series ◽  
Variational Iteration ◽  
Homotopy Perturbation ◽  
Quadratic Integral ◽  
Quadratic Integral Equations

In this paper, the approximate solutions for  quadratic integral equations (QIEs) are given by the variational iteration method(VIM) and homotopy perturbation method (HPM). These methods produce the solutions in terms of convergent series without needing to restrictive assumptions, to illustrate the ability and credibility of the methods, we deal with some examples that show simplicity and effectiveness.

scholarly journals Hypersingular integral equations of the first kind: A modified homotopy perturbation method and its application to vibration and active control

2019 ◽  
Vol 38 (2) ◽  
pp. 706-727 ◽  
Author(s):  
Reza Novin ◽  
Mohammad Ali Fariborzi Araghi
Keyword(s):  
Perturbation Method ◽  
Integral Equations ◽  
Homotopy Perturbation Method ◽  
The Novel ◽  
Validity And Reliability ◽  
Hypersingular Integral ◽  
Homotopy Perturbation ◽  
Hypersingular Integral Equations ◽  
Ideal Tool ◽  
Novel Method

This paper attempts to propose and investigate a modification of the homotopy perturbation method to study hypersingular integral equations of the first kind. Along with considering this matter, of course, the novel method has been compared with the standard homotopy perturbation method. This method can be conveniently fast to get the exact solutions. The validity and reliability of the proposed scheme are discussed. Different examples are included to prove so. According to the results, we further state that new simple homotopy perturbation method is so efficient and promises the exact solution. The modification of the homotopy perturbation method has been discovered to be the significant ideal tool in dealing with the complicated function-theoretic analytical structures within an analytical method.

scholarly journals An analytical technique for solving general linear integral equations of the second kind and its application in analysis of flash lamp control circuit

2014 ◽  
Vol 62 (3) ◽  
pp. 413-421 ◽  
Author(s):  
E. Hetmaniok ◽  
D. Słota ◽  
T. Trawiński ◽  
R. Wituła
Keyword(s):  
Approximate Solution ◽  
Perturbation Method ◽  
Integral Equations ◽  
Homotopy Perturbation Method ◽  
General Linear ◽  
Practical Application ◽  
Analytical Technique ◽  
Homotopy Perturbation ◽  
Linear Integral ◽  
Linear Integral Equations

Abstract In this paper an application of the homotopy perturbation method for solving the general linear integral equations of the second kind is discussed. It is shown that under proper assumptions the considered equation possesses a unique solution and the series obtained in the homotopy perturbation method is convergent. The error of approximate solution, received by taking only the partial sum of the series, is also estimated. Moreover, there is presented an example of applying the method for approximate solution of an equation which has a practical application for charge calculation in supply circuit of the flash lamps used in cameras.

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