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 |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 1026-0226 1607-887X |