Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1120.65108
Ganji, D.D.; Sadighi, A.
Application of homotopy-perturbation and variational iteration methods to nonlinear heat transfer and porous media equations. (English)
[J] J. Comput. Appl. Math. 207, No. 1, 24-34 (2007). ISSN 0377-0427

Summary: Perturbation methods depend on a small parameter which is difficult to be found for real-life nonlinear problems. To overcome this shortcoming, two new but powerful analytical methods are introduced to solve nonlinear heat transfer problems in this article; one is {\it J.-H. He}'s variational iteration method [(VIM); Int. J. Non-Linear Mech. 34, No. 4, 699--708 (1999; Zbl 05137891)] and the other is {\it J.-H. He}'s homotopy-perturbation method [(HPM); Comput. Methods Appl. Mech. Eng. 178, No. 3--4, 257--262 (1999; Zbl 0956.70017)]. The VIM is to construct correction functionals using general Lagrange multipliers identified optimally via the variational theory, and the initial approximations can be freely chosen with unknown constants. The HPM deforms a difficult problem into a simple problem which can be easily solved. Nonlinear convective-radiative cooling equation, nonlinear heat equation (porous media equation) and nonlinear heat equation with cubic nonlinearity are used as examples to illustrate the simple solution procedures. Comparison of the applied methods with exact solutions reveals that both methods are tremendously effective.

MSC 2000:: *65M70 Spectral, collocation and related methods (IVP of PDE)
35K55 Nonlinear parabolic equations

Keywords: heat transfer; nonlinear equations; variational iteration method; homotopy-perturbation method; numerical examples; nonlinear heat equation; porous media equation

Citations: Zbl 05137891; Zbl 0956.70017

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]