Interpolants for Runge-Kutta formulas-Reference-Cited by-同舟云学术

Interpolants for Runge-Kutta formulas

Published:1986-09 Issue:3 Volume:12 Page:193-218
ISSN:0098-3500
Container-title:ACM Transactions on Mathematical Software
language:en
Short-container-title:ACM Trans. Math. Softw.

Author:

Enright W. H.¹,Jackson K. R.¹,Nørsett S. P.²,Thomsen P. G.³

Affiliation:

1. Univ. of Toronto, Toronto, Ont., Canada

2. Technical Univ. of Norway, Trondheim, Norway

3. Technical Univ. of Denmark, Lyngby, Denmark

Abstract

A general procedure for the construction of interpolants for Runge-Kutta (RK) formulas is presented. As illustrations, this approach is used to develop interpolants for three explicit RK formulas, including those employed in the well-known subroutines RKF45 and DVERK. A typical result is that no extra function evaluations are required to obtain an interpolant with O ( h 5 ) local truncation error for the fifth-order RK formula used in RKF45; two extra function evaluations per step are required to obtain an interpolant with O ( h 6 ) local truncation error for this RK formula.

Publisher

Association for Computing Machinery (ACM)

Subject

Applied Mathematics,Software

Link

https://dl.acm.org/doi/pdf/10.1145/7921.7923

Reference19 articles.

1. Coefficients for the study of Runge-Kutta integration processes

2. DORMAND J. R. AND PRINCE P. J. Runge-Kutta triples. Manuscript Mathematics Dept. Teesside Polytechnic Middlesbrough U.K. 1986. DORMAND J. R. AND PRINCE P. J. Runge-Kutta triples. Manuscript Mathematics Dept. Teesside Polytechnic Middlesbrough U.K. 1986.

3. ENRIGHT W. H. AND JACKSON K. R. NORSETr S. P. AND THOMSEN P.G. Effective solution of discontinuous IVPs using a Runge-Kutta formula pair with interpolants. Rep. 113 Mathematics Dept. Univ. of Manchester U.K. 1986. Submitted for publication. ENRIGHT W. H. AND JACKSON K. R. NORSETr S. P. AND THOMSEN P.G. Effective solution of discontinuous IVPs using a Runge-Kutta formula pair with interpolants. Rep. 113 Mathematics Dept. Univ. of Manchester U.K. 1986. Submitted for publication.

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