Uniform enclosure of high order of boundary value problems by monotone discretization-Reference-Cited by-同舟云学术

Uniform enclosure of high order of boundary value problems by monotone discretization

Published:1989 Issue:188 Volume:53 Page:609-617
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Grossmann Ch.,Roos H.-G.

Abstract

In the investigation of boundary value problems the construction of a two-sided inclusion of the solution can be as important as a numerical approximation of the solution itself. In the present paper we analyze a monotone discretization technique of higher order based upon piecewise interpolation and shifting such that bounding upper and lower solutions are obtained. The monotone discretization under consideration takes advantage of the property of the operator to be of monotone kind.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/1989-53-188/S0025-5718-1989-0983561-7/S0025-5718-1989-0983561-7.pdf

Reference13 articles.

1. E. Adams, Invers-Monotonie, Direkte und Indirekte Intervallmethoden, Bericht Nr. 185, Forschungszentrum Graz., 1982.

2. E. Adams & H. Spreuer, "Konvergente numerische Schrankenkonstruktionen mit Spline-Funktionen für nichtlineare gewöhnliche bzw. lineare parabolische Randwertaufgaben," in Interval Mathematics (K. Nickel, ed.), Springer-Verlag, Berlin, 1975.

3. Studies in Mathematics and its Applications, Vol. 4;Ciarlet, Philippe G.,1978

4. Monotone discretization of two-point boundary value problems and related numerical methods;Grossmann, Ch.,1987

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1. An analytically oriented discretization technique for boundary value problems;Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg;1991-12