**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**31105

##### Investigation of a Transition from Steady Convection to Chaos in Porous Media Using Piecewise Variational Iteration Method

**Authors:**
Mohamed M. Mousa,
Aidarkhan Kaltayev Shahwar F. Ragab

**Abstract:**

In this paper, a new dependable algorithm based on an adaptation of the standard variational iteration method (VIM) is used for analyzing the transition from steady convection to chaos for lowto-intermediate Rayleigh numbers convection in porous media. The solution trajectories show the transition from steady convection to chaos that occurs at a slightly subcritical value of Rayleigh number, the critical value being associated with the loss of linear stability of the steady convection solution. The VIM is treated as an algorithm in a sequence of intervals for finding accurate approximate solutions to the considered model and other dynamical systems. We shall call this technique as the piecewise VIM. Numerical comparisons between the piecewise VIM and the classical fourth-order Runge–Kutta (RK4) numerical solutions reveal that the proposed technique is a promising tool for the nonlinear chaotic and nonchaotic systems.

**Keywords:**
Chaos,
free convection,
variational iteration method,
Lorenz equations

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1062510

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