𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Exact solutions of nonlinear diffusion equations by variational iteration method

✍ Scribed by A. Sadighi; D.D. Ganji

Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
654 KB
Volume
54
Category
Article
ISSN
0898-1221

No coin nor oath required. For personal study only.

✦ Synopsis

In this paper, He's variational iteration method is applied to obtain exact solutions of some nonlinear diffusion equations. The variational iteration method is used 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 solutions obtained are compared with those obtained by the Adomian decomposition method and homotopy perturbation method, showing excellent agreement, but the variational iteration method is more effective. He's variational iteration method can be introduced to overcome the difficulties arising in calculating Adomian polynomials.

πŸ“œ SIMILAR VOLUMES

Exact special solutions to the nonlinear
Exact special solutions to the nonlinear dispersive and equations by He’s variational iteration method
✍ Mustafa Inc πŸ“‚ Article πŸ“… 2008 πŸ› Elsevier Science 🌐 English βš– 614 KB

We implemented a variational method for approximating the solution to the nonlinear dispersive K (m, p, 1)-type equations. By using this scheme, the explicit exact solution is calculated in the form of a quickly convergent series with easily computable components. To illustrate the application of th

The variational iteration method: A powe
The variational iteration method: A powerful scheme for handling linear and nonlinear diffusion equations
✍ Abdul-Majid Wazwaz πŸ“‚ Article πŸ“… 2007 πŸ› Elsevier Science 🌐 English βš– 181 KB

In this work, we introduce a framework for obtaining exact solutions to linear and nonlinear diffusion equations. Exact solutions are developed for some diffusion processes of power law diffusitivies. He's variational iteration method (VIM) is used for analytic treatment of these equations. The powe

Exact solutions of some nonlinear partia
Exact solutions of some nonlinear partial differential equations using the variational iteration method linked with Laplace transforms and the PadΓ© technique
✍ Tamer A. Abassy; Magdy A. El-Tawil; H. El-Zoheiry πŸ“‚ Article πŸ“… 2007 πŸ› Elsevier Science 🌐 English βš– 666 KB

In this paper, the variational iteration method (VIM) is reintroduced with Laplace transforms and the PadΓ© technique treatment to obtain closed form solutions of nonlinear equations. Some examples, including the coupled Burger's equation, compacton k(n, n) equation, Zakharov-Kuznetsov Zk(n, n) equat