Direct Solution of nth-Order IVPs by Homotopy Analysis Method
Direct solution of a class of nth-order initial value problems (IVPs) is considered based on the homotopy analysis method (HAM). The HAM solutions contain an auxiliary parameter which provides a convenient way of controlling the convergence region of the series solutions. The HAM gives approximate a...
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| Published in | Differential Equations and Nonlinear Mechanics Vol. 2009; no. 2009; pp. 48 - 62 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Cairo, Egypt
Hindawi Limiteds
01.01.2009
Hindawi Puplishing Corporation Hindawi Publishing Corporation Hindawi Limited |
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| Abstract | Direct solution of a class of nth-order initial value problems (IVPs) is considered based on the homotopy analysis method (HAM). The HAM solutions contain an auxiliary parameter which provides a convenient way of controlling the convergence region of the series solutions. The HAM gives approximate analytical solutions which are of comparable accuracy to the seven- and eight-order Runge-Kutta method (RK78). |
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| AbstractList | Direct solution of a class of nth -order initial value problems (IVPs) is considered based on the homotopy analysis method (HAM). The HAM solutions contain an auxiliary parameter which provides a convenient way of controlling the convergence region of the series solutions. The HAM gives approximate analytical solutions which are of comparable accuracy to the seven- and eight-order Runge-Kutta method (RK78). |
| Author | M. S. M. Noorani I. Hashim A. Sami Bataineh |
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| Contributor | Hashim, Ishak Noorani, Mohd. Salmi Md |
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| Copyright | Copyright © 2009 Copyright © 2009 A. Sami Bataineh et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. |
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| DOI | 10.1155/2009/842094 |
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| References | (3) 1995; 30 (8) 2005; 169 (30) 2007; 8 (6) 2004; 147 (10) 2003; 41 (4) 1997; 32 (21) 2008; 372 LiaoS.-J.The proposed homotopy analysis techniques for the solution of nonlinear problems, Ph.D. dissertation1992Shanghai, ChinaShanghai Jiao Tong University (7) 2004; 47 (18) 2009; 14 (24) 2009; 14 (33) 1992; 28 (25) 2009; 14 (28) 2007; 204 (22) 2008; 2008 (15) 2006; 15 (13) 2008; 13 (5) 1999; 34 (11) 2004; 168 (17) 2008; 29 31 (19) 2008; 13 (20) 2007; 371 (23) 2008; 55 (26) 2007; 40 (27) 2005; 26 (9) 2005; 48 (16) 2008; 136 LiaoS.-J.Beyond Perturbation: Introduction to the Homotopy Analysis Method20042Boca Raton, Fla, USAChapman & Hall/CRCxii+322CRC Series: Modern Mechanics and MathematicsMR2058313 (12) 2005; 42 (29) 2005; 42 (32) 2003; 135 (14) 2006; 360 |
| References_xml | – volume: 47 start-page: 75 issue: 1 year: 2004 end-page: 85 ident: 7 article-title: Explicit analytic solution for similarity boundary layer equations – volume: 26 start-page: 963 issue: 3 year: 2005 end-page: 978 ident: 27 article-title: A variable step Runge-Kutta-Nyström integrator for reversible systems of second order initial value problems – volume: 147 start-page: 499 issue: 2 year: 2004 end-page: 513 ident: 6 article-title: On the homotopy analysis method for nonlinear problems – volume: 30 start-page: 371 issue: 3 year: 1995 end-page: 380 ident: 3 article-title: An approximate solution technique not depending on small parameters: a special example – volume: 360 start-page: 109 issue: 1 year: 2006 end-page: 113 ident: 14 article-title: The application of homotopy analysis method to nonlinear equations arising in heat transfer – volume: 29 start-page: 223 issue: 2 year: 2008 end-page: 228 ident: 17 article-title: A new modification of false position method based on homotopy analysis method – volume: 14 start-page: 430 issue: 2 year: 2009 end-page: 442 ident: 18 article-title: Modified homotopy analysis method for solving systems of second-order BVPs – volume: 136 start-page: 144 issue: 2-3 year: 2008 end-page: 150 ident: 16 article-title: Approximate solution for the nonlinear model of diffusion and reaction in porous catalysts by means of the homotopy analysis method – volume: 34 start-page: 759 issue: 4 year: 1999 end-page: 778 ident: 5 article-title: An explicit, totally analytic approximate solution for Blasius' viscous flow problems – volume: 135 start-page: 73 issue: 1 year: 2003 end-page: 79 ident: 32 article-title: Homotopy perturbation method: a new nonlinear analytical technique – volume: 32 start-page: 815 issue: 5 year: 1997 end-page: 822 ident: 4 article-title: A kind of approximate solution technique which does not depend upon small parameters. 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| Snippet | Direct solution of a class of nth-order initial value problems (IVPs) is considered based on the homotopy analysis method (HAM). The HAM solutions contain an... Direct solution of a class of nth -order initial value problems (IVPs) is considered based on the homotopy analysis method (HAM). The HAM solutions contain an... |
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| Title | Direct Solution of nth-Order IVPs by Homotopy Analysis Method |
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