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From the fitting techniques to accurate schemes for the Liouville-Bratu-Gelfand problem. (English) Zbl 1099.65098

Summary: 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 [cf. R. Buckmire, Numer. Methods Partial Differ. Equations 20, No. 3, 327–337 (2004; Zbl 1048.65102)] 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.

MSC:

65N06 Finite difference methods for boundary value problems involving PDEs
35J65 Nonlinear boundary value problems for linear elliptic equations
80A25 Combustion

Citations:

Zbl 1048.65102
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References:

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