메뉴 건너뛰기




Volumn 41, Issue 2, 2006, Pages 161-171

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

Author keywords

Adaptive step size control; Automatic differentiation; Differential algebraic equations; Initial value problems; Structural analysis; Taylor series

Indexed keywords


EID: 33646473882     PISSN: 10171398     EISSN: 15729265     Source Type: Journal    
DOI: 10.1007/s11075-005-9007-1     Document Type: Article
Times cited : (9)

References (25)
  • 2
    • 0016939583 scopus 로고
    • Fast multiple-precision evaluation of elementary functions
    • R.P. Brent, Fast multiple-precision evaluation of elementary functions, J. Assoc. Comput. Mach 23(2) (1976) 242-251.
    • (1976) J. Assoc. Comput. Mach , vol.23 , Issue.2 , pp. 242-251
    • Brent, R.P.1
  • 5
    • 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) 115-124.
    • (2002) Numer. Algorithms , vol.31 , pp. 115-124
    • Corless, R.M.1
  • 6
    • 0141468113 scopus 로고    scopus 로고
    • An elementary solution of a minimax problem arising in algorithms for automatic mesh selection
    • R.M. Corless, An elementary solution of a minimax problem arising in algorithms for automatic mesh selection, SIGSAM Bulletin: Commun. Comput. Algebra 34(4) (2001) 7-15.
    • (2001) SIGSAM Bulletin: Commun. Comput. Algebra , vol.34 , Issue.4 , pp. 7-15
    • Corless, R.M.1
  • 8
    • 0020143282 scopus 로고
    • Solving ordinary differential equations using Taylor series
    • G. Corliss and Y.F. Chang, Solving ordinary differential equations using Taylor series, ACM Tansactions on Mathematical Software 8(2) (1982) 114-144.
    • (1982) ACM Tansactions on Mathematical Software , vol.8 , Issue.2 , pp. 114-144
    • Corliss, G.1    Chang, Y.F.2
  • 9
    • 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) 288-301.
    • (1989) Appl. Math. Comput. , vol.31 , pp. 288-301
    • Enright, W.H.1
  • 10
    • 0034509771 scopus 로고    scopus 로고
    • Continuous numerical methods for ODEs with defect control
    • W.H. Enright, Continuous numerical methods for ODEs with defect control, J. Comp. Appl. Math 125(1-2) (2000) 159-170.
    • (2000) J. Comp. Appl. Math , vol.125 , Issue.1-2 , pp. 159-170
    • Enright, W.H.1
  • 12
    • 0036679644 scopus 로고    scopus 로고
    • Some recent advances in validated methods for IVPs for ODEs
    • K.R. Jackson and N. Nedialkov, Some recent advances in validated methods for IVPs for ODEs, Appl. Numer. Math. 42(1) (2002) 269-284.
    • (2002) Appl. Numer. Math. , vol.42 , Issue.1 , pp. 269-284
    • Jackson, K.R.1    Nedialkov, N.2
  • 13
    • 0012912813 scopus 로고
    • Solving ordinary differential equations I
    • Springer, Berlin Heidelberg New York
    • E. Hairer, S.P. Norsett, G. Wanner, Solving Ordinary Differential Equations I, Computational Mathematics Vol. 8, (Springer, Berlin Heidelberg New York 1987).
    • (1987) Computational Mathematics , vol.8
    • Hairer, E.1    Norsett, S.P.2    Wanner, G.3
  • 14
    • 0002690510 scopus 로고
    • Solving ordinary differential equations II
    • Springer, Berlin Heidelberg New York
    • E. Hairer and G. Wanner, Solving Ordinary Differential Equations II, Computational Mathematics, Vol. 14, (Springer, Berlin Heidelberg New York 1991).
    • (1991) Computational Mathematics , vol.14
    • Hairer, E.1    Wanner, G.2
  • 15
    • 0010942489 scopus 로고
    • Handheld calculator evaluates integrals
    • W. Kahan, Handheld calculator evaluates integrals, Hewlett-Packard J. 31(8) (1980) 23-32.
    • (1980) Hewlett-Packard J. , vol.31 , Issue.8 , pp. 23-32
    • Kahan, W.1
  • 16
    • 0004924333 scopus 로고    scopus 로고
    • Are we there yet? Zero crossing and event handling for differential equations
    • C. Moler, Are we there yet? Zero crossing and event handling for differential equations, Matlab News & Notes (1997) 16-17.
    • (1997) Matlab News & Notes , pp. 16-17
    • Moler, C.1
  • 17
    • 33646467140 scopus 로고    scopus 로고
    • Solving differential-algebraic equations by Taylor series (1): Computing Taylor coefficients
    • accepted
    • N.S. Nedialkov and J.D. Pryce, Solving differential-algebraic equations by Taylor series (1): computing Taylor coefficients, BIT, accepted.
    • BIT
    • Nedialkov, N.S.1    Pryce, J.D.2
  • 18
    • 33646490662 scopus 로고    scopus 로고
    • N.S.Nedialkov, Private Communication
    • N.S.Nedialkov, Private Communication.
  • 20
    • 0041331524 scopus 로고    scopus 로고
    • A simple structural analysis method for DAEs
    • J.D. Pryce, A simple structural analysis method for DAEs. BIT 41(2) (2001) 364-394.
    • (2001) BIT , vol.41 , Issue.2 , pp. 364-394
    • Pryce, J.D.1
  • 21
    • 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) 195-211.
    • (1998) Numer. Algorithms , vol.19 , pp. 195-211
    • Pryce, J.D.1
  • 22
    • 9544230707 scopus 로고    scopus 로고
    • Solving ODEs and DDEs with residual control
    • L. Shampine, Solving ODEs and DDEs with residual control, Appl. Numer. Math 52(1) (2005) 113-127.
    • (2005) Appl. Numer. Math , vol.52 , Issue.1 , pp. 113-127
    • Shampine, L.1
  • 23
    • 0033190030 scopus 로고    scopus 로고
    • Solving index-1 DAEs in matlab and simulink
    • L.F. Shampine, M.W. Reichelt and J.A. Kierzenka, Solving Index-1 DAEs in Matlab and Simulink, SIAM Rev. 41(3) (1999) 538-552.
    • (1999) SIAM Rev. , vol.41 , Issue.3 , pp. 538-552
    • Shampine, L.F.1    Reichelt, M.W.2    Kierzenka, J.A.3
  • 24
    • 0036441379 scopus 로고    scopus 로고
    • Automatic control and adaptive time-stepping
    • ]24] G. Söderlind, Automatic control and adaptive time-stepping, Numer. Algorithms 31 (2002) 281-310.
    • (2002) Numer. Algorithms , vol.31 , pp. 281-310
    • Söderlind, G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.