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Numerical method for the wave and nonlinear diffusion equations with the homotopy perturbation method

✍ Scribed by Changbum Chun; Hossein Jafari; Yong-Il Kim

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
386 KB
Volume
57
Category
Article
ISSN
0898-1221

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✦ Synopsis

diffusion equations Approximate analytical solution Exact solutions a b s t r a c t

In this paper, the homotopy perturbation method and a modified homotopy perturbation method are used for analytical treatment of the wave equation and some nonlinear diffusion equations, respectively. Some examples are given to illustrate that a suitable choice of an initial solution can lead to the exact solution, this revealing the reliability and effectiveness of the method.

πŸ“œ SIMILAR VOLUMES

Homotopy analysis method for solving lin
Homotopy analysis method for solving linear and nonlinear fractional diffusion-wave equation
✍ H. Jafari; S. Seifi πŸ“‚ Article πŸ“… 2009 πŸ› Elsevier Science 🌐 English βš– 196 KB

In this paper, we adopt the homotopy analysis method (HAM) to obtain solutions of linear and nonlinear fractional diffusion and wave equation. The fractional derivative is described in the Caputo sense. Some illustrative examples are presented.

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Homotopy analysis method for solving multi-term linear and nonlinear diffusion–wave equations of fractional order
✍ H. Jafari; A. Golbabai; S. Seifi; K. Sayevand πŸ“‚ Article πŸ“… 2010 πŸ› Elsevier Science 🌐 English βš– 531 KB

In this paper we have used the homotopy analysis method (HAM) to obtain solutions of multi-term linear and nonlinear diffusion-wave equations of fractional order. The fractional derivative is described in the Caputo sense. Some illustrative examples have been presented.