Construction of Efficient General Linear Methods for Non-Stiff Differential Systems

被引：18

作者：

Bras, Michal ^{[1
,2
]}

Cardone, Angelamaria ^{[3
]}

机构：

[1] AGH Univ Sci & Technol, Fac Appl Math, PL-30059 Krakow, Poland

[2] Jagiellonian Univ, Fac Math & Comp Sci, PL-30348 Krakow, Poland

[3] Univ Salerno, Dipartimento Matemat, I-84084 Fisciano, SA, Italy

来源：

MATHEMATICAL MODELLING AND ANALYSIS | 2012年 / 17卷 / 02期

关键词：

general linear methods; Nordsieck representation; order conditions; inherent quadratic stability; region of absolute stability; RUNGE-KUTTA METHODS;

D O I：

10.3846/13926292.2012.655789

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper describes the construction of explicit general linear methods in Nordsieck form with inherent quadratic stability and large areas of the stability region. After satisfying order and inherent quadratic stability conditions, the remaining free parameters are used to find the methods with large area of region of absolute stability. Examples of methods with p = q+1 = s = r and p = q = s = r - 1 up to order 6 are given.

引用

页码：171 / 189

页数：19

共 17 条

[1] [Anonymous], 2002, THESIS U AUCKLAND NZ
[2] [Anonymous], APPL NUMER MATH
[3] Nordsieck representation of two-step Runge-Kutta methods for ordinary differential equations
Bartoszewski, Z
Jackiewicz, Z
[J]. APPLIED NUMERICAL MATHEMATICS, 2005, 53 (2-4) : 149 - 163
[4] Construction of two-step Runge-Kutta methods of high order for ordinary differential equations
Bartoszewski, Z
Jackiewicz, Z
[J]. NUMERICAL ALGORITHMS, 1998, 18 (01) : 51 - 70
[5] Nordsieck methods with computationally verified algebraic stability
Bras, M.
Jackiewicz, Z.
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2011, 217 (21) : 8598 - 8610
[6] Nordsieck Methods with Inherent Quadratic Stability
Bras, M.
[J]. MATHEMATICAL MODELLING AND ANALYSIS, 2011, 16 (01) : 82 - 96
[7] Butcher J. C., 2003, Numerical Methods for Ordinary Differential Equations, V2nd, DOI DOI 10.1002/9780470753767
[8] Construction of general linear methods with Runge-Kutta stability properties
Butcher, JC
Jackiewicz, Z
[J]. NUMERICAL ALGORITHMS, 2004, 36 (01) : 53 - 72
[9] The construction of practical general linear methods
Butcher, JC
Wright, WM
[J]. BIT NUMERICAL MATHEMATICS, 2003, 43 (04) : 695 - 721
[10] DIAGONALLY IMPLICIT GENERAL LINEAR METHODS FOR ORDINARY DIFFERENTIAL-EQUATIONS
BUTCHER, JC
JACKIEWICZ, Z
[J]. BIT, 1993, 33 (03): : 452 - 472

← 1 2 →