Higham, D.J. (1991) Runge-Kutta defect control using Hermite-Birkhoff interpolation. SIAM Journal on Scientific Computing, 12 (5). pp. 991-999. ISSN 1064-8275Full text not available in this repository. (Request a copy from the Strathclyde author)
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.
|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|
|Depositing user:||Ms Sarah Scott|
|Date Deposited:||09 Mar 2006|
|Last modified:||29 Apr 2016 00:04|