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From the fitting techniques to accurate schemes for the Liouville‐Bratu‐Gelfand problem
Author(s) -
Mounim A. Serghini,
de Dormale B.M.
Publication year - 2006
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20116
Subject(s) - mathematics , scheme (mathematics) , construct (python library) , mathematical optimization , mathematical analysis , computer science , programming language
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. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006