Higham, D.J. (1991) Highly continuous Runge-Kutta interpolants. ACM Transactions on Mathematical Software, 17 (3). pp. 368-386. ISSN 0098-3500Full text not available in this repository. (Request a copy from the Strathclyde author)
To augment the discrete Runge-Kutta solutlon to the mitlal value problem, piecewlse Hermite interpolants have been used to provide a continuous approximation with a continuous first derivative We show that it M possible to construct mterpolants with arbltrardy many continuous derivatives which have the same asymptotic accuracy and basic cost as the Hermite interpol ants. We also show that the usual truncation coefficient analysis can be applied to these new interpolants, allowing their accuracy to be examined in more detad As an Illustration, we present some globally C2 interpolants for use with a popular 4th and 5th order Runge-Kutta pair of Dormand and Prince, and we compare them theoretically and numerically with existing interpolants.
|Keywords:||performance, reliability, runge-kutta methods, numerical mathematics, Mathematics, Software, Applied Mathematics|
|Subjects:||Science > Mathematics|
|Department:||Faculty of Science > Mathematics and Statistics|
|Depositing user:||Ms Sarah Scott|
|Date Deposited:||08 Mar 2006|
|Last modified:||22 Mar 2017 09:02|