Application of He's Homotopy Perturbation Method for Cauchy Problem of Ill-Posed Nonlinear Diffusion Equation
We consider a Cauchy problem of unidimensional nonlinear diffusion equation on finite interval. This problem is ill-posed and its approximate solution is unstable. We apply the He's homotopy perturbation method (HPM) and obtain the third-order asymptotic expansion. We show that if the conductiv...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2010/780207 |
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| _version_ | 1849683488969588736 |
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| author | Ali Zakeri Azim Aminataei Qodsiyeh Jannati |
| author_facet | Ali Zakeri Azim Aminataei Qodsiyeh Jannati |
| author_sort | Ali Zakeri |
| collection | DOAJ |
| description | We consider a Cauchy problem of unidimensional
nonlinear diffusion equation on finite interval. This problem is ill-posed
and its approximate solution is unstable. We apply the He's homotopy
perturbation method (HPM) and obtain the third-order asymptotic expansion. We show that if the conductivity term in diffusion equation has
a specified condition, the above solution can be estimated. Finally, a
numerical experiment is provided to illustrate the method. |
| format | Article |
| id | doaj-art-d877fe3bf9de49529d15a3a3ad0d2153 |
| institution | DOAJ |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-d877fe3bf9de49529d15a3a3ad0d21532025-08-20T03:23:51ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2010-01-01201010.1155/2010/780207780207Application of He's Homotopy Perturbation Method for Cauchy Problem of Ill-Posed Nonlinear Diffusion EquationAli Zakeri0Azim Aminataei1Qodsiyeh Jannati2Department of Mathematics, K. N. Toosi University of Technology, P.O. Box 16315-1618, 1541849611 Tehran, IranDepartment of Mathematics, K. N. Toosi University of Technology, P.O. Box 16315-1618, 1541849611 Tehran, IranDepartment of Mathematics, K. N. Toosi University of Technology, P.O. Box 16315-1618, 1541849611 Tehran, IranWe consider a Cauchy problem of unidimensional nonlinear diffusion equation on finite interval. This problem is ill-posed and its approximate solution is unstable. We apply the He's homotopy perturbation method (HPM) and obtain the third-order asymptotic expansion. We show that if the conductivity term in diffusion equation has a specified condition, the above solution can be estimated. Finally, a numerical experiment is provided to illustrate the method.http://dx.doi.org/10.1155/2010/780207 |
| spellingShingle | Ali Zakeri Azim Aminataei Qodsiyeh Jannati Application of He's Homotopy Perturbation Method for Cauchy Problem of Ill-Posed Nonlinear Diffusion Equation Discrete Dynamics in Nature and Society |
| title | Application of He's Homotopy Perturbation Method for Cauchy Problem of Ill-Posed Nonlinear Diffusion Equation |
| title_full | Application of He's Homotopy Perturbation Method for Cauchy Problem of Ill-Posed Nonlinear Diffusion Equation |
| title_fullStr | Application of He's Homotopy Perturbation Method for Cauchy Problem of Ill-Posed Nonlinear Diffusion Equation |
| title_full_unstemmed | Application of He's Homotopy Perturbation Method for Cauchy Problem of Ill-Posed Nonlinear Diffusion Equation |
| title_short | Application of He's Homotopy Perturbation Method for Cauchy Problem of Ill-Posed Nonlinear Diffusion Equation |
| title_sort | application of he s homotopy perturbation method for cauchy problem of ill posed nonlinear diffusion equation |
| url | http://dx.doi.org/10.1155/2010/780207 |
| work_keys_str_mv | AT alizakeri applicationofheshomotopyperturbationmethodforcauchyproblemofillposednonlineardiffusionequation AT azimaminataei applicationofheshomotopyperturbationmethodforcauchyproblemofillposednonlineardiffusionequation AT qodsiyehjannati applicationofheshomotopyperturbationmethodforcauchyproblemofillposednonlineardiffusionequation |