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Monotonic piecewise cubic interpolation, with applications to ODE plotting

Higham, D.J. (1992) Monotonic piecewise cubic interpolation, with applications to ODE plotting. Journal of Computational and Applied Mathematics, 39 (3). pp. 287-294. ISSN 0377-0427

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Abstract

Given a set of solution and derivative values, we examine the problem of constructing a piecewise cubic interpolant which reflects the monotonicity present in the data. Drawing on the theory of Fritsch and Carlson (1980), we derive a simple algorithm that, if necessary, adds one or two extra knots between existing knots in order to preserve monotonicity. The new algorithm is completely local in nature and does not perturb the input data. We show that the algorithm is particularly suited to the case where the data arises from the discrete approximate solution of an ODE.

Item type: Article
ID code: 203
Keywords: Cubic polynomial, Hermite, interpolation, monotonicity, initial-value problem, numerical mathematics, Mathematics
Subjects: Science > Mathematics
Department: Faculty of Science > Mathematics and Statistics
Related URLs:
    Depositing user: Ms Sarah Scott
    Date Deposited: 09 Mar 2006
    Last modified: 12 Mar 2012 10:35
    URI: http://strathprints.strath.ac.uk/id/eprint/203

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