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 0377-0427Full text not available in this repository. (Request a copy from the Strathclyde author)
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.
|Keywords:||Cubic polynomial, Hermite, interpolation, monotonicity, initial-value problem, numerical mathematics, Mathematics, Computational Mathematics, Applied Mathematics|
|Subjects:||Science > Mathematics|
|Department:||Faculty of Science > Mathematics and Statistics|
|Depositing user:||Ms Sarah Scott|
|Date Deposited:||09 Mar 2006|
|Last modified:||06 Jan 2017 03:01|