THE ANALYSIS OF GENERALIZED BACKWARDS DIFFERENCE FORMULA METHODS APPLIED TO HESSENBERG FORM DIFFERENTIAL-ALGEBRAIC EQUATIONS

被引：12

作者：

KEIPER, JB ^{[1
]}

GEAR, CW ^{[1
]}

机构：

[1] NEC RES INST INC,PRINCETON,NJ 08540

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 1991年 / 28卷 / 03期

关键词：

BACKWARD DIFFERENCE FORMULA; DIFFERENTIAL-ALGEBRAIC EQUATION;

D O I：

10.1137/0728044

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The numerical solution of Hessenberg form differential-algebraic equations by variable stepsize, generalized backward difference formulae (GBDF) is studied. GBDF methods of sufficiently high order are shown to converge for problems of index 3 and 4. The proof techniques developed are not sufficiently powerful to show convergence for index 5 problems, although it is speculated that convergence also occurs for these problems.

引用

页码：833 / 858

页数：26

共 50 条

[41] Stability of an implicit difference scheme for a linear differential-algebraic system of partial differential equations
S. V. Gaidomak
Computational Mathematics and Mathematical Physics, 2010, 50 : 673 - 683
[42] PARALLEL GENERAL LINEAR METHODS FOR STIFF ORDINARY DIFFERENTIAL AND DIFFERENTIAL-ALGEBRAIC EQUATIONS
BUTCHER, JC
CHARTIER, P
APPLIED NUMERICAL MATHEMATICS, 1995, 17 (03) : 213 - 222
[43] Asymptotic stability analysis of Runge–Kutta methods for differential-algebraic equations with multiple delays
Meijun Wu
Quanhong Yu
Jiaoxun Kuang
Hongjiong Tian
Calcolo, 2021, 58
[44] PROJECTED IMPLICIT RUNGE-KUTTA METHODS FOR DIFFERENTIAL-ALGEBRAIC EQUATIONS
ASCHER, UM
PETZOLD, LR
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1991, 28 (04) : 1097 - 1120
[45] STABILITY OF NUMERICAL-METHODS FOR DIFFERENTIAL-ALGEBRAIC EQUATIONS OF HIGHER INDEX
ARNOLD, M
APPLIED NUMERICAL MATHEMATICS, 1993, 13 (1-3) : 5 - 14
[46] Numerical comparison of methods for solving fractional differential-algebraic equations (FDAEs)
Ibis, Birol
Bayram, Mustafa
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2011, 62 (08) : 3270 - 3278
[47] Steady-state methods of differential-algebraic equations in circuit simulation
Jiang, YL
JOURNAL OF CIRCUITS SYSTEMS AND COMPUTERS, 2005, 14 (02) : 383 - 393
[48] On convergence conditions of waveform relaxation methods for linear differential-algebraic equations
Bai, Zhong-Zhi
Yang, Xi
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2011, 235 (08) : 2790 - 2804
[49] A theory of symmetric one-step methods for differential-algebraic equations
Kulikov, GY
RUSSIAN JOURNAL OF NUMERICAL ANALYSIS AND MATHEMATICAL MODELLING, 1997, 12 (06) : 501 - 523
[50] Asymptotic stability of linear delay differential-algebraic equations and numerical methods
Zhu, WJ
Petzold, LR
APPLIED NUMERICAL MATHEMATICS, 1997, 24 (2-3) : 247 - 264

← 1 2 3 4 5 →