On the homoclinic orbit for convection in a fluid layer heated from below

The homoclinic orbit associated with the transition from steady convection to Chaos in the weak turbulent regime is difficult to recover in simple com putational procedures because of its unstable nature. A simple procedure wh ich recovers the homoclinic orbit up to the desired accuracy is presented. This procedure combines the insight obtained from previous work on a local non-linear analysis of the problem and the Adomian's decomposition method o f solution which provides a global semi-analytical solution, (C) 1999 Elsev ier Science Ltd. All rights reserved.