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.
@article{104356, author = {Hans-G\"org Roos}, title = {Uniformly enclosing discretization methods and grid generation for semilinear boundary value problems with first order terms}, journal = {Applications of Mathematics}, volume = {34}, year = {1989}, pages = {274-284}, zbl = {0685.65069}, mrnumber = {1008580}, language = {en}, url = {http://dml.mathdoc.fr/item/104356} }
Roos, Hans-Görg. Uniformly enclosing discretization methods and grid generation for semilinear boundary value problems with first order terms. Applications of Mathematics, Tome 34 (1989) pp. 274-284. http://gdmltest.u-ga.fr/item/104356/
Konvergente numerische Schrankenkonstruktionen mit SplineFunktionen für nichtlineare gewöhnliche bzw. liheare parabolische Randwertaufgaben, "Int. Math." (ed: K. Nickel), Berlin, Springer-Verlag 1975. (1975)
Gleichmäßig einschließende Diskretisierungsverfahren für schwach nichtlineare Randwertaufgaben, Numer. Math., 49 (1986), 95-110. (1986) | Article | MR 0847020
Uniformly enclosing discretization methods of high order for boundary value problems, (submitted to Math. Comput.).
Feedback grid generation via monotone discretization for two-point boundary value problems, IMA J. Numer. Anal. 6 (1986), 421-432. (1986) | Article | MR 0968268
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. (1987) | MR 0950227
Iterationsverfahren zur Lösung schwach nichtlinearer elliptischer Randwertaufgaben mit monotoner Lösungseinschließung, Diss., TU Dresden 1983. (1983)
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. (1979) | Article | MR 0620075 | Zbl 0404.65050