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Runge-Kutta defect control using Hermite-Birkhoff interpolation

Higham, D.J. (1991) Runge-Kutta defect control using Hermite-Birkhoff interpolation. SIAM Journal on Scientific Computing, 12 (5). pp. 991-999. ISSN 1064-8275

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Abstract

Two techniques for reliably controlling the defect (residual) in the numerical solution of nonstifi initial value problems were given in [D. J. Higham, SIAM J. Numer. Anal., 26(1989), pp. 1175-1183]. This work describes an alternative approach based on Hermite-Birkhofi interpolation. The new approach has two main advantages-it is applicable to Runge-Kutta schemes of any order, and it gives rise to a defect of the optimum asymptotic order of accuracy. For a particular Runge-Kutta formula the asymptotic analysis is verified numerically.

Item type: Article
ID code: 208
Keywords: Runge–Kutta, defect, residual, backward error, Hermite–Birkhofi interpolation, numerical mathematics, Probabilities. Mathematical statistics, Computational Mathematics, Applied Mathematics
Subjects: Science > Mathematics > Probabilities. Mathematical statistics
Department: Faculty of Science > Mathematics and Statistics
Related URLs:
    Depositing user: Ms Sarah Scott
    Date Deposited: 09 Mar 2006
    Last modified: 04 Sep 2014 09:53
    URI: http://strathprints.strath.ac.uk/id/eprint/208

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