| Title:
|
Uniformly enclosing discretization methods and grid generation for semilinear boundary value problems with first order terms (English) |
| Author:
|
Roos, Hans-Görg |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
34 |
| Issue:
|
4 |
| Year:
|
1989 |
| Pages:
|
274-284 |
| Summary lang:
|
English |
| Summary lang:
|
Russian |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper deals with uniformly enclosing discretization methods of the first order for semilinear boundary value problems. Some fundamental properties of this discretization technique (the enclosing property, convergence, the inverse-monotonicity) are proved. A feedback grid generation principle using information from the lower and upper solutions is presented. (English) |
| Keyword:
|
uniformly enclosing discretization methods |
| Keyword:
|
grid generation |
| Keyword:
|
semilinear |
| Keyword:
|
enclosure |
| Keyword:
|
boundary value problem |
| MSC:
|
34B15 |
| MSC:
|
65L10 |
| MSC:
|
65L50 |
| idZBL:
|
Zbl 0685.65069 |
| idMR:
|
MR1008580 |
| DOI:
|
10.21136/AM.1989.104356 |
| . |
| Date available:
|
2008-05-20T18:36:58Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104356 |
| . |
| Reference:
|
[1] E. Adams H. Spreuer: Konvergente numerische Schrankenkonstruktionen mit SplineFunktionen für nichtlineare gewöhnliche bzw. liheare parabolische Randwertaufgaben."Int. Math." (ed: K. Nickel), Berlin, Springer-Verlag 1975. |
| Reference:
|
[2] Ch. Großmann M. Krätzschmar H.-G. Roos: Gleichmäßig einschließende Diskretisierungsverfahren für schwach nichtlineare Randwertaufgaben.Numer. Math., 49 (1986), 95-110. MR 0847020, 10.1007/BF01389432 |
| Reference:
|
[3] Ch. Großmann M. Krätzschmar H.-G. Roos: Uniformly enclosing discretization methods of high order for boundary value problems.(submitted to Math. Comput.). |
| Reference:
|
[4] Ch. Großmann H.-G. Roos: Feedback grid generation via monotone discretization for two-point boundary value problems.IMA J. Numer. Anal. 6 (1986), 421-432. MR 0968268, 10.1093/imanum/6.4.421 |
| Reference:
|
[5] Ch. Großmann: Monotone discretization of two-point boundary value problems and related numerical methods.In: Adams, Ansorge, Großmann, Roos (eds.): Discretization of differential equations and enclosures, Akademie-Verlag, Berlin 1987. MR 0950227 |
| Reference:
|
[6] M. Krätzschmar: Iterationsverfahren zur Lösung schwach nichtlinearer elliptischer Randwertaufgaben mit monotoner Lösungseinschließung.Diss., TU Dresden 1983. |
| Reference:
|
[7] K. Nickel: The construction of a priori bounds for the solution of a two-point boundary value problem with finite elements I.Computing 23 (1979), 247-265. Zbl 0404.65050, MR 0620075, 10.1007/BF02252131 |
| . |
