메뉴 건너뛰기




Volumn 48, Issue 1, 2008, Pages 29-49

Polynomial cost for solving IVP for high-index DAE

Author keywords

Adaptive step size control; Automatic differentiation; Differential algebraic equations; H lder mean; Initial value problem; Structural analysis; Taylor series

Indexed keywords


EID: 41049109334     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10543-008-0163-2     Document Type: Article
Times cited : (8)

References (38)
  • 3
    • 13544262350 scopus 로고    scopus 로고
    • Performance of the Taylor series methods for ODEs/DAEs
    • 2
    • R. Barrio, Performance of the Taylor series methods for ODEs/DAEs, Appl. Math. Comput., 163(2) (2005), pp. 525-545.
    • (2005) Appl. Math. Comput. , vol.163 , pp. 525-545
    • Barrio, R.1
  • 4
    • 27544484059 scopus 로고    scopus 로고
    • VSVO formulation of the Taylor method for the numerical solution of ODEs
    • 1-2
    • R. Barrio, F. Blesa, and M. Lara, VSVO formulation of the Taylor method for the numerical solution of ODEs, Comput. Math. Appl., 50(1-2) (2005), pp. 93-111.
    • (2005) Comput. Math. Appl. , vol.50 , pp. 93-111
    • Barrio, R.1    Blesa, F.2    Lara, M.3
  • 9
    • 0141468113 scopus 로고    scopus 로고
    • An elementary solution of a minimax problem arising in algorithms for automatic mesh selection
    • 4
    • R. M. Corless, An elementary solution of a minimax problem arising in algorithms for automatic mesh selection, SIGSAM Bull.: Commun. Comput. Algebra, 34(4) (2001), pp. 7-15.
    • (2001) SIGSAM Bull.: Commun. Comput. Algebra , vol.34 , pp. 7-15
    • Corless, R.M.1
  • 10
    • 0036439121 scopus 로고    scopus 로고
    • A new view of the computational complexity of IVP for ODE
    • R. M. Corless, A new view of the computational complexity of IVP for ODE, Numer. Algorithms, 31 (2002), pp. 115-124.
    • (2002) Numer. Algorithms , vol.31 , pp. 115-124
    • Corless, R.M.1
  • 11
    • 0020143282 scopus 로고
    • Solving ordinary differential equations using Taylor series
    • 2
    • G. Corliss and Y. F. Chang, Solving ordinary differential equations using Taylor series, ACM Trans. Math. Softw., 8(2) (1982), pp. 114-144.
    • (1982) ACM Trans. Math. Softw. , vol.8 , pp. 114-144
    • Corliss, G.1    Chang, Y.F.2
  • 12
    • 84980075420 scopus 로고
    • Interior estimates for elliptic systems of partial differential equations
    • A. Douglis and L. Nirenberg, Interior estimates for elliptic systems of partial differential equations, Commun. Pure Appl. Math., 8 (1955), pp. 503-538.
    • (1955) Commun. Pure Appl. Math. , vol.8 , pp. 503-538
    • Douglis, A.1    Nirenberg, L.2
  • 13
    • 0001743435 scopus 로고
    • A new error control for initial value solvers
    • W. H. Enright, A new error control for initial value solvers, Appl. Math. Comput., 31 (1989), pp. 288-301.
    • (1989) Appl. Math. Comput. , vol.31 , pp. 288-301
    • Enright, W.H.1
  • 16
    • 0003319841 scopus 로고    scopus 로고
    • Evaluating derivatives: Principles and techniques of algorithmic differentiation
    • SIAM, Philadelphia, PA
    • A. Griewank, Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation, Frontiers in Applied Mathematics, SIAM, Philadelphia, PA, 2000.
    • (2000) Frontiers in Applied Mathematics
    • Griewank, A.1
  • 17
    • 0012912813 scopus 로고
    • Solving Ordinary Differential Equations i
    • Springer Berlin
    • E. Hairer, S. P. Nørsett, and G. Wanner, Solving Ordinary Differential Equations I, Comput. Math., vol. 8, Springer, Berlin, 1987.
    • (1987) Comput. Math. , vol.8
    • Hairer, E.1    Nørsett, S.P.2    Wanner, G.3
  • 18
    • 0002690510 scopus 로고
    • Solving ordinary differential equations II
    • Springer Berlin
    • E. Hairer and G. Wanner, Solving Ordinary Differential Equations II, Comput. Math., vol. 14, Springer, Berlin, 1991.
    • (1991) Comput. Math. , vol.14
    • Hairer, E.1    Wanner, G.2
  • 20
    • 0345867387 scopus 로고    scopus 로고
    • Fast evaluation of holonomic functions
    • J. van der Hoeven, Fast evaluation of holonomic functions, Theor. Comput. Sci., 210 (1999), pp. 199-215.
    • (1999) Theor. Comput. Sci. , vol.210 , pp. 199-215
    • Van Der Hoeven, J.1
  • 22
    • 33646473882 scopus 로고    scopus 로고
    • Numerical solutions of index-1 differential algebraic equations can be computed in polynomial time
    • 2
    • S. Ilie, R. M. Corless, and G. Reid, Numerical solutions of index-1 differential algebraic equations can be computed in polynomial time, Numer. Algorithms, 41(2) (2006), pp. 161-171.
    • (2006) Numer. Algorithms , vol.41 , pp. 161-171
    • Ilie, S.1    Corless, R.M.2    Reid, G.3
  • 23
    • 44649201223 scopus 로고    scopus 로고
    • Adaptivity and computational complexity in the numerical solution of ODEs
    • doi:10.1016/j.jco.2007.11.004
    • S. Ilie, G. Söderlind, and R. M. Corless, Adaptivity and computational complexity in the numerical solution of ODEs, J. Complexity (in press). doi:10.1016/j.jco.2007.11.004
    • J. Complexity (In Press)
    • Ilie, S.1    Söderlind, G.2    Corless, R.M.3
  • 24
    • 0036679644 scopus 로고    scopus 로고
    • Some recent advances in validated methods for IVPs for ODEs
    • 1
    • K. R. Jackson and N. Nedialkov, Some recent advances in validated methods for IVPs for ODEs, Appl. Numer. Math., 42(1) (2002), pp. 269-284.
    • (2002) Appl. Numer. Math. , vol.42 , pp. 269-284
    • Jackson, K.R.1    Nedialkov, N.2
  • 26
    • 0004293209 scopus 로고
    • Prentice Hall, Englewood Cliffs New York
    • R. E. Moore, Interval Analysis, Prentice Hall, Englewood Cliffs, New York, 1966.
    • (1966) Interval Analysis
    • Moore, R.E.1
  • 27
    • 41049108854 scopus 로고    scopus 로고
    • private communication
    • N. S. Nedialkov, private communication.
    • Nedialkov, N.S.1
  • 28
    • 28144454918 scopus 로고    scopus 로고
    • Solving differential-algebraic equations by Taylor series (I): Computing Taylor coefficients
    • 3
    • N. S. Nedialkov and J. D. Pryce, Solving differential-algebraic equations by Taylor series (I): computing Taylor coefficients, BIT, 45(3) (2005), pp. 561-591.
    • (2005) BIT , vol.45 , pp. 561-591
    • Nedialkov, N.S.1    Pryce, J.D.2
  • 29
    • 0000353268 scopus 로고
    • The consistent initialization of differential-algebraic systems
    • 2
    • C. Pantelides, The consistent initialization of differential-algebraic systems, SIAM J. Sci. Stat. Comput., 9(2) (1988), pp. 213-231.
    • (1988) SIAM J. Sci. Stat. Comput. , vol.9 , pp. 213-231
    • Pantelides, C.1
  • 30
    • 0032262788 scopus 로고    scopus 로고
    • Solving high-index DAEs by Taylor series
    • J. D. Pryce, Solving high-index DAEs by Taylor series, Numer. Algorithms, 19 (1998), pp. 195-211.
    • (1998) Numer. Algorithms , vol.19 , pp. 195-211
    • Pryce, J.D.1
  • 31
    • 0041331524 scopus 로고    scopus 로고
    • A simple structural analysis method for DAEs
    • 2
    • J. D. Pryce, A simple structural analysis method for DAEs, BIT, 41(2) (2001), pp. 364-394.
    • (2001) BIT , vol.41 , pp. 364-394
    • Pryce, J.D.1
  • 32
    • 41049101235 scopus 로고    scopus 로고
    • private communication
    • J. D. Pryce, private communication.
    • Pryce, J.D.1
  • 35
    • 0036441379 scopus 로고    scopus 로고
    • Automatic control and adaptive time-stepping
    • G. Söderlind, Automatic control and adaptive time-stepping, Numer. Algorithms, 31 (2002), pp. 281-310.
    • (2002) Numer. Algorithms , vol.31 , pp. 281-310
    • Söderlind, G.1
  • 37
    • 36349031172 scopus 로고    scopus 로고
    • Symbolic-numeric computation of implicit Riquier bases for PDE
    • ACM
    • W. Wu and G. Reid, Symbolic-numeric computation of implicit Riquier bases for PDE, Proc. of ISSAC 2007, ACM (2007), pp. 377-386.
    • (2007) Proc. of ISSAC 2007 , pp. 377-386
    • Wu, W.1    Reid, G.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.