Application of homotopy-perturbation and variational iteration methods to nonlinear heat transfer and porous media equations

By D. Domiri Ganji, A. Sadighi. 2007

290 citations recorded by the source corpus.

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 He's variational iteration method (VIM) and the other is the homotopy-perturbation method (HPM). 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.

Subfields: Biomedical Engineering, Mechanics of Materials, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/a2a0935fe89fc12b043d4374ae1c98c0d8006f1b

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In Biomedical Engineering

In Mechanics of Materials

In Modeling and Simulation

Citations in the corpus

Variational iteration method: New development and applications (2007, background): “to axisymmetrical flow over a stretching sheet [34], D’Acunto [35,36], Xu [37], Draganescu [38], Ganji and Sadighi to nonlinear heat transfer [39], Marinca [40] and He [1] to nonlinear oscillators, Draganescu and Capalnasan to nonlinear relaxation phenomena in polycrystalline solids [38], Lu to two-”
SOLUTION OF AN INTEGRO-DIFFERENTIAL EQUATION ARISING IN OSCILLATING MAGNETIC FIELDS USING HE'S HOMOTOPY PERTURBATION METHOD (2008, unknown): “This method has been employed to solve a large variety of linear and nonlinear problems such as fractional partial differential equations [32], the nonlinear HirotaSatsuma coupled KdV partial differential equation [12], nonlinear boundary value problems [22], traveling wave solutions of nonlinear wa”
HOMOTOPY PERTURBATION METHOD FOR THREE-DIMENSIONAL PROBLEM OF CONDENSATION FILM ON INCLINED ROTATING DISK (2012, methodology): “Recently, this method has been employed for much research in engineering sciences [9–17].”