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Numerical methods for second order singular pertubation problems

✍ Scribed by F. Mazzia; D. Trigiante

Publisher
Elsevier Science
Year
1992
Tongue
English
Weight
375 KB
Volume
23
Category
Article
ISSN
0898-1221

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✦ Synopsis

By using sufficient conditions which ensure the well conditioning of tridiagonal matrices, we derive numerical methods for second order singular perturbations boundary values problems. Under hypotheses similar to the ones usually used in the continuous theory, methods are derived which use constant step sizes h ~ 0(el/2). In the more general case methods with variable step sizes, axe defined which solve the problem with n(~ e-l) steps. Examples on standard test problems are shown.

πŸ“œ SIMILAR VOLUMES

Higher order uniformly convergent method
Higher order uniformly convergent methods for singular perturbation problems
✍ Hans-GΓΆrg Roos πŸ“‚ Article πŸ“… 1994 πŸ› Elsevier Science 🌐 English βš– 367 KB

Until now, the best way to construct high order uniformly convergent schemes for singular perturbation problems was to apply exponentially fitted compact difference schemes. We propose the following approach: firstly solve an auxiliary problem with piecewise or nearly piecewise constant coefficients