Numerical solutions of index-1 differential algebraic equations can be computed in polynomial time

被引：10
|
作者：
Ilie, S [1 ]
Corless, RM
Reid, G
机构：
[1] Univ Western Ontario, Ontario Res Ctr Comp Algebra, London, ON N6A 5B7, Canada
[2] Univ Western Ontario, Dept Appl Math, London, ON N6A 5B7, Canada
来源：
NUMERICAL ALGORITHMS | 2006年 / 41卷 / 02期
基金：
加拿大自然科学与工程研究理事会;
关键词：
differential algebraic equations; initial value problems; adaptive step-size control; Taylor series; structural analysis; automatic differentiation;
D O I：
10.1007/s11075-005-9007-1
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The cost of solving an initial value problem for index-1 differential algebraic equations to accuracy epsilon is polynomial in ln(1/epsilon). This cost is obtained for an algorithm based on the Taylor series method for solving differential algebraic equations developed by Pryce. This result extends a recent result by Corless for solutions of ordinary differential equations. The results of the standard theory of information-based complexity give exponential cost for solving ordinary differential equations, being based on a different model.
引用
收藏
页码：161 / 171
页数：11
相关论文
共 50 条
  • [1] Numerical solutions of index-1 differential algebraic equations can be computed in polynomial time
    Silvana Ilie
    Robert M. Corless
    Greg Reid
    Numerical Algorithms, 2006, 41 : 161 - 171
  • [2] Fractional step methods for index-1 differential-algebraic equations
    Vijalapura, PK
    Strain, J
    Govindjee, S
    JOURNAL OF COMPUTATIONAL PHYSICS, 2005, 203 (01) : 305 - 320
  • [3] LYAPUNOV SPECTRUM OF NONAUTONOMOUS LINEAR STOCHASTIC DIFFERENTIAL ALGEBRAIC EQUATIONS OF INDEX-1
    Nguyen Dinh Cong
    Nguyen Thi The
    STOCHASTICS AND DYNAMICS, 2012, 12 (04)
  • [4] Multirate implicit Euler schemes for a class of differential–algebraic equations of index-1
    Hachtel, Christoph
    Bartel, Andreas
    Günther, Michael
    Sandu, Adrian
    Journal of Computational and Applied Mathematics, 2021, 387
  • [5] Convergence and stability of numerical solutions to a class of index 1 stochastic differential algebraic equations with time delay
    Qu, Xiaomei
    Huang, Chengming
    Liu, Chao
    APPLIED MATHEMATICS AND COMPUTATION, 2010, 215 (11) : 4008 - 4021
  • [6] POLYNOMIAL CHAOS FOR SEMIEXPLICIT DIFFERENTIAL ALGEBRAIC EQUATIONS OF INDEX 1
    Pulch, Roland
    INTERNATIONAL JOURNAL FOR UNCERTAINTY QUANTIFICATION, 2013, 3 (01) : 1 - 23
  • [7] Continuation method for computing certain singular points for index-1 differential algebraic equations
    Attili, Basem S.
    APPLIED MATHEMATICS AND COMPUTATION, 2006, 175 (02) : 1026 - 1038
  • [8] A note on discrete waveform relaxation of stiff index-1 differential algebraic equations & Symposia
    Sun, Wei
    Fan, Xiao-Guang
    2013 10TH IEEE INTERNATIONAL CONFERENCE ON CONTROL AND AUTOMATION (ICCA), 2013, : 502 - 506
  • [9] Multirate implicit Euler schemes for a class of differential-algebraic equations of index-1
    Hachtel, Christoph
    Bartel, Andreas
    Guenther, Michael
    Sandu, Adrian
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2021, 387
  • [10] Regularization of index-1 differential-algebraic equations with rank-deficient constraints
    Moore, PK
    Petzold, LR
    Ren, Y
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1998, 35 (05) : 43 - 61
12345