Towards a code for nonstiff differential systems based on general linear methods with inherent Runge-Kutta stability

被引：16

作者：

Abdi, A. ^{[1
]}

Jackiewicz, Z. ^{[2
,3
]}

机构：

[1] Univ Tabriz, Fac Math Sci, Tabriz, Iran

[2] Arizona State Univ, Sch Math & Stat Sci, Tempe, AZ 85287 USA

[3] AGH Univ Sci & Technol, Dept Appl Math, Krakow, Poland

来源：

APPLIED NUMERICAL MATHEMATICS | 2019年 / 136卷

关键词：

General linear methods; Nordsieck representation; Inherent Runge-Kutta stability; Adaptive stepsize and order selection; CONSTRUCTION;

D O I：

10.1016/j.apnum.2018.10.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Various issues are discussed which are relevant to the development of the code for nonstiff differential systems based on a class of general linear methods with inherent Runge-Kutta stability. (C) 2018 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：103 / 121

页数：19

共 17 条

[1] [Anonymous], 1998, CWI Quarterly
[2] [Anonymous], THESIS
[3] Error propagation of general linear methods for ordinary differential equations
Butcher, J. C.
Jackiewicz, Z.
Wright, W. M.
[J]. JOURNAL OF COMPLEXITY, 2007, 23 (4-6) : 560 - 580
[4] Unconditionally stable general linear methods for ordinary differential equations
Butcher, JC
Jackiewicz, Z
[J]. BIT NUMERICAL MATHEMATICS, 2004, 44 (03) : 557 - 570
[5] Construction of general linear methods with Runge-Kutta stability properties
Butcher, JC
Jackiewicz, Z
[J]. NUMERICAL ALGORITHMS, 2004, 36 (01) : 53 - 72
[6] The construction of practical general linear methods
Butcher, JC
Wright, WM
[J]. BIT NUMERICAL MATHEMATICS, 2003, 43 (04) : 695 - 721
[7] A new approach to error estimation for general linear methods
Butcher, JC
Jackiewicz, Z
[J]. NUMERISCHE MATHEMATIK, 2003, 95 (03) : 487 - 502
[8] Experiments with a variable-order type 1 DIMSIM code
Butcher, JC
Chartier, P
Jackiewicz, Z
[J]. NUMERICAL ALGORITHMS, 1999, 22 (3-4) : 237 - 261
[9] CONTROL THEORETIC TECHNIQUES FOR STEPSIZE SELECTION IN EXPLICIT RUNGE-KUTTA METHODS
GUSTAFSSON, K
[J]. ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE, 1991, 17 (04): : 533 - 554
[10] A PI-STEPSIZE CONTROL FOR THE NUMERICAL-SOLUTION OF ORDINARY DIFFERENTIAL-EQUATIONS
GUSTAFSSON, K
LUNDH, M
SODERLIND, G
[J]. BIT, 1988, 28 (02): : 270 - 287

← 1 2 →