A posteriori error estimation and global error control for ordinary differential equations by the adjoint method

被引：40

作者：

Cao, Y ^{[1
]}

Petzold, L ^{[1
]}

机构：

[1] Univ Calif Santa Barbara, Dept Comp Sci, Santa Barbara, CA 93106 USA

来源：

SIAM JOURNAL ON SCIENTIFIC COMPUTING | 2004年 / 26卷 / 02期

关键词：

adjoint method; ordinary differential equation; global error control;

D O I：

10.1137/S1064827503420969

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we propose a general method for a posteriori error estimation in the solution of initial value problems in ordinary differential equations (ODEs). With the help of adjoint sensitivity software, this method can be implemented efficiently. It provides a condition estimate for the ODE system. We also propose an algorithm for global error control, based on the condition of the system and the perturbation due to the numerical approximation.

引用

页码：359 / 374

页数：16

共 33 条

[1]

Becker R, 2001, ACT NUMERIC, V10, P1, DOI 10.1017/S0962492901000010

[2] Adaptive finite element methods for optimal control of partial differential equations: Basic concept [J].

Becker, R ;

Kapp, H ;

Rannacher, R .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2000, 39 (01) :113-132

[3] An optimal control approach to adaptivity in computational fluid mechanics [J].

Becker, R ;

Heuveline, V ;

Rannacher, R .

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, 2002, 40 (1-2) :105-120

[4]

BRENAN KE, 1995, CLASSICS APPL MATH, V14

[5] VODE - A VARIABLE-COEFFICIENT ODE SOLVER [J].

BROWN, PN ;

BYRNE, GD ;

HINDMARSH, AC .

SIAM JOURNAL ON SCIENTIFIC AND STATISTICAL COMPUTING, 1989, 10 (05) :1038-1051

[6] A subspace error estimate or linear systems [J].

Cao, Y ;

Petzold, L .

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2003, 24 (03) :787-801

[7] Adjoint sensitivity analysis for differential-algebraic equations: algorithms and software [J].

Cao, Y ;

Li, ST ;

Petzold, L .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2002, 149 (01) :171-191

[8] ADJOINT SENSITIVITY ANALYSIS FOR DIFFERENTIAL-ALGEBRAIC EQUATIONS: THE ADJOINT DAE SYSTEM AND ITS NUMERICAL SOLUTION [J].

Cao, Yang ;

Li, Shengtai ;

Petzold, Linda ;

Serban, Radu .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2003, 24 (03) :1076-1089

[9]

DAHLQUIST G, 1981, LECT NOTES MATH, V912, P38

[10]

Estep D, 2000, SIAM J SCI COMPUT, V21, P1609

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