Homotopy Analysis Method Based on Optimal Value of the Convergence Control Parameter for Solving Semi-Differential Equations

Homotopy Analysis Method Based on Optimal Value of the Convergence Control Parameter for Solving Semi-Differential Equations

In this paper, homotopy analysis method is directly extended to investigate nth order semi-differential equations and to derive their numerical solutions which is introduced by replacing some integer-order space derivatives by fractional derivatives. The fractional derivatives are described in t...

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Main Authors: H. Hosseini Fadravi∗, H. Saberi Nik, R. Buzhabadi
Format: Article
Language:English
Published: Islamic Azad University 2011-09-01
Series:Journal of Mathematical Extension
Online Access:http://ijmex.com/index.php/ijmex/article/view/92
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spelling doaj-647fc730f64041aaad94aaaf9f5808db2020-11-25T03:42:22ZengIslamic Azad UniversityJournal of Mathematical Extension1735-82991735-82992011-09-0153105121Homotopy Analysis Method Based on Optimal Value of the Convergence Control Parameter for Solving Semi-Differential EquationsH. Hosseini Fadravi∗0H. Saberi Nik1R. Buzhabadi2Islamic Azad University, Neyshabur BranchIslamic Azad University, Neyshabur BranchR. BuzhabadiIn this paper, homotopy analysis method is directly extended to investigate nth order semi-differential equations and to derive their numerical solutions which is introduced by replacing some integer-order space derivatives by fractional derivatives. The fractional derivatives are described in the Caputo sense. So the homotopy analysis method for differential equations of integer-order is directly extended to derive explicit and numerical solutions of the fractional differential equations. An optimal value of the convergence control parameter is given through the square residual error. Comparison is made between Homotopy perturbation method, collocation spline method, and the present methodhttp://ijmex.com/index.php/ijmex/article/view/92
collection DOAJ
language English
format Article
sources DOAJ
author H. Hosseini Fadravi∗
H. Saberi Nik
R. Buzhabadi
spellingShingle H. Hosseini Fadravi∗
H. Saberi Nik
R. Buzhabadi
Homotopy Analysis Method Based on Optimal Value of the Convergence Control Parameter for Solving Semi-Differential Equations
Journal of Mathematical Extension
author_facet H. Hosseini Fadravi∗
H. Saberi Nik
R. Buzhabadi
author_sort H. Hosseini Fadravi∗
title Homotopy Analysis Method Based on Optimal Value of the Convergence Control Parameter for Solving Semi-Differential Equations
title_short Homotopy Analysis Method Based on Optimal Value of the Convergence Control Parameter for Solving Semi-Differential Equations
title_full Homotopy Analysis Method Based on Optimal Value of the Convergence Control Parameter for Solving Semi-Differential Equations
title_fullStr Homotopy Analysis Method Based on Optimal Value of the Convergence Control Parameter for Solving Semi-Differential Equations
title_full_unstemmed Homotopy Analysis Method Based on Optimal Value of the Convergence Control Parameter for Solving Semi-Differential Equations
title_sort homotopy analysis method based on optimal value of the convergence control parameter for solving semi-differential equations
publisher Islamic Azad University
series Journal of Mathematical Extension
issn 1735-8299
1735-8299
publishDate 2011-09-01
description In this paper, homotopy analysis method is directly extended to investigate nth order semi-differential equations and to derive their numerical solutions which is introduced by replacing some integer-order space derivatives by fractional derivatives. The fractional derivatives are described in the Caputo sense. So the homotopy analysis method for differential equations of integer-order is directly extended to derive explicit and numerical solutions of the fractional differential equations. An optimal value of the convergence control parameter is given through the square residual error. Comparison is made between Homotopy perturbation method, collocation spline method, and the present method
url http://ijmex.com/index.php/ijmex/article/view/92
work_keys_str_mv AT hhosseinifadravi homotopyanalysismethodbasedonoptimalvalueoftheconvergencecontrolparameterforsolvingsemidifferentialequations
AT hsaberinik homotopyanalysismethodbasedonoptimalvalueoftheconvergencecontrolparameterforsolvingsemidifferentialequations
AT rbuzhabadi homotopyanalysismethodbasedonoptimalvalueoftheconvergencecontrolparameterforsolvingsemidifferentialequations
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