From the fitting techniques to accurate schemes for the Liouville-Bratu-Gelfand problem

We are interested in numerical methods for the Liouville-Bratu-Gelfand problem. The ideas and techniques developed here to construct the schemes are inspired from the fitted method and the so-called compact exponentially fitted method. Some of those schemes can be viewed as extensions of both the Buckmire scheme and the standard scheme which results from the use of the standard finite-difference procedures. We study and compare computationally the accuracy of methods introduced here. It is also mentioned that the Buckmire's techniques and the standard scheme are a particular case of the fitted method. (C) 2005 Wiley Periodicals, Inc.