Isomeric trees and the order of Runge-Kutta methods

被引：0

作者：

Butcher, John C. ^{[1
]}

Podhaisky, Helmut ^{[2
]}

机构：

[1] Univ Auckland, Dept Math, Auckland, New Zealand

[2] Martin Luther Univ Halle Wittenberg, Inst Math, Halle, Germany

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2022年 / 415卷

关键词：

Runge-Kutta method; Scalar; Non-autonomous; Order condition;

D O I：

10.1016/j.cam.2022.114480

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The conditions for a Runge-Kutta method to be of order p with p >= 5 for a scalar non-autonomous problem are a proper subset of the order conditions for a vector problem. Nevertheless, Runge-Kutta methods that were derived historically only for scalar problems happened to be of the same order for vector problems. We relate the order conditions for scalar problems to factorisations of the Runge-Kutta trees into "atomic stumps" and enumerate those conditions up to p = 20. Using a special search procedure over unsatisfied order conditions, new Runge-Kutta methods of "ambiguous orders" five and six are constructed. These are used to verify the validity of the results. (C) 2022 The Author(s). Published by Elsevier B.V.

引用

页数：8

共 9 条

[1] Berland H, 2005, CRM PROC & LECT NOTE, V39, P49
[2] Butcher J.C., 2021, B SERIES ALGEBRAIC A
[3] BUTCHER JC, 1963, J AUSTR MATH SOC, V3, P202, DOI DOI 10.1017/S1446788700027944
[4] Trees, Stumps, and Applications
Butcher, John C.
[J]. AXIOMS, 2018, 7 (03)
[5] Heun K., 1900, Z. Math. Phys., V45, P23
[6] Kutta W., 1901, Z MATH PHYS, V46, P435
[7] Nystrom E., 1925, ACTA SOC SCI FENN, V50, P1
[8] Runge-Kutta pairs for scalar autonomous initial value problems
Papageorgiou, G
Tsitouras, C
[J]. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2003, 80 (02) : 201 - 209
[9] Runge C., 1895, MATH ANN, V46, P167, DOI 10.1007/BF01446807

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