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


Authors: Ch. Grossmann and H.-G. Roos
Journal: Math. Comp. 53 (1989), 609-617
MSC: Primary 65L10
DOI: https://doi.org/10.1090/S0025-5718-1989-0983561-7
MathSciNet review: 983561
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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.


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DOI: https://doi.org/10.1090/S0025-5718-1989-0983561-7
Article copyright: © Copyright 1989 American Mathematical Society

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