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IPM
30
YEARS OLD

“School of Mathematics”

Paper   IPM / M / 8725
   School of Mathematics
  Title: Solution of a partial differential equation subject to temperature overspecification by He's homotopy perturbation method
  Author(s): M. Dehghan (Joint with F. Shakeri)
  Status: Published
  Journal: Physica Scripta
  Vol.: 75
  Year: 2007
  Pages: 778-787
  Supported by: IPM
  Abstract:
In this work, the solution of an inverse problem concerning a diffusion equation with source control parameters is presented. The homotopy perturbation method is employed to solve this equation. This method changes a difficult problem into a simple problem which can be easily solved. In this procedure, according to the homotopy technique, a homotopy with an embedding parameter pE [0, 1] is constructed, and this parameter is considered a 'small parameter', so the method is called the homotopy perturbation method, which can take full advantage of the traditional perturbation method and homotopy technique. The approxi�mations obtained by the proposed method are uniformly valid not only for small parameters, but also for very large parameters. The fact that this technique, in contrast to the traditional perturbation methods, does not require a small parameter in the system, leads to wide applications in nonlinear equations.

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