Article
Full entry |
PDF
(1.2 MB)
Feedback
PDF
(1.2 MB)
Feedback
Keywords:
uniformly enclosing discretization methods; grid generation; semilinear; enclosure; boundary value problem
uniformly enclosing discretization methods; grid generation; semilinear; enclosure; boundary value problem
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.
References:
[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.
[2] Ch. Großmann M. Krätzschmar H.-G. Roos: Gleichmäßig einschließende Diskretisierungsverfahren für schwach nichtlineare Randwertaufgaben. Numer. Math., 49 (1986), 95-110. DOI 10.1007/BF01389432 | MR 0847020
[3] Ch. Großmann M. Krätzschmar H.-G. Roos: Uniformly enclosing discretization methods of high order for boundary value problems. (submitted to Math. Comput.).
[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. DOI 10.1093/imanum/6.4.421 | MR 0968268
[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
[6] M. Krätzschmar: Iterationsverfahren zur Lösung schwach nichtlinearer elliptischer Randwertaufgaben mit monotoner Lösungseinschließung. Diss., TU Dresden 1983.
[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. DOI 10.1007/BF02252131 | MR 0620075 | Zbl 0404.65050
Search
Partner of
