A nonlinear optimization approach to the construction of general linear methods of high order

被引：30

作者：

Butcher, JC

Jackiewicz, Z

Mittelmann, HD

机构：

[1] UNIV AUCKLAND,DEPT MATH & STAT,AUCKLAND,NEW ZEALAND

[2] ARIZONA STATE UNIV,DEPT MATH,TEMPE,AZ 85287

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 1997年 / 81卷 / 02期

基金：

美国国家科学基金会;

关键词：

general linear method; ordinary differential equation; A-stability; L-stability; least-squares minimization;

D O I：

10.1016/S0377-0427(97)00039-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We describe the construction of diagonally implicit multistage integration methods of order and stage order p = q = 7 and p = q = 8 for ordinary differential equations. These methods were obtained using state-of-the-art optimization methods, particularly variable-model trust-region least-squares algorithms.

引用

页码：181 / 196

页数：16

共 22 条

[1] *AT T LAB, 1984, PORT MATH SUBR LIB
[2] BISCHOF C, 1994, ANLMCSP4811194
[3] ALGORITHM-717 SUBROUTINES FOR MAXIMUM-LIKELIHOOD AND QUASI-LIKELIHOOD ESTIMATION OF PARAMETERS IN NONLINEAR-REGRESSION MODELS
BUNCH, DS
GAY, DM
WELSCH, RE
[J]. ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE, 1993, 19 (01): : 109 - 130
[4] DIAGONALLY-IMPLICIT MULTISTAGE INTEGRATION METHODS
BUTCHER, JC
[J]. APPLIED NUMERICAL MATHEMATICS, 1993, 11 (05) : 347 - 363
[5] Construction of diagonally implicit general linear methods of type 1 and 2 for ordinary differential equations
Butcher, JC
Jackiewicz, Z
[J]. APPLIED NUMERICAL MATHEMATICS, 1996, 21 (04) : 385 - 415
[6] DIAGONALLY IMPLICIT GENERAL LINEAR METHODS FOR ORDINARY DIFFERENTIAL-EQUATIONS
BUTCHER, JC
JACKIEWICZ, Z
[J]. BIT, 1993, 33 (03): : 452 - 472
[7] GENERALIZED PADE APPROXIMATIONS TO THE EXPONENTIAL FUNCTION
BUTCHER, JC
CHIPMAN, FH
[J]. BIT, 1992, 32 (01): : 118 - 130
[8] BUTCHER JC, IN PRESS SIAM J NUME
[9] BUTCHER JC, UNPUB NORDSIECK REPR
[10] BUTCHER JC, UNPUB CONSTRUCTION H

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