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Volumn 57, Issue 10, 2007, Pages 1145-1162

Validated solutions of initial value problems for parametric ODEs

Author keywords

Dynamic systems; Interval analysis; Ordinary differential equations; Taylor models; Validated computing

Indexed keywords

DYNAMICAL SYSTEMS; NUMERICAL METHODS; ORDINARY DIFFERENTIAL EQUATIONS; PARAMETER ESTIMATION; PROBLEM SOLVING; SOFTWARE PACKAGES;

EID: 34047210346     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2006.10.006     Document Type: Article
Times cited : (172)

References (35)
  • 1
    • 34547187330 scopus 로고    scopus 로고
    • C. Bendsten, O. Stauning, FADBAD, a flexible C++ package for automatic differentiation using the forward and backward methods, Technical Report 1996-x5-94, Technical University of Denmark, Lyngby, Denmark, 1996
  • 2
    • 34547179582 scopus 로고    scopus 로고
    • C. Bendsten, O. Stauning, TADIFF, a flexible C++ package for automatic differentiation using Taylor series, Technical Report 1997-x5-94, Technical University of Denmark, Lyngby, Denmark, 1997
  • 3
    • 0000329979 scopus 로고    scopus 로고
    • Verified integration of ODEs and flows using differential algebraic methods on high-order Taylor models
    • Berz M., and Makino K. Verified integration of ODEs and flows using differential algebraic methods on high-order Taylor models. Reliable Computing 4 (1998) 361-369
    • (1998) Reliable Computing , vol.4 , pp. 361-369
    • Berz, M.1    Makino, K.2
  • 5
    • 0003279959 scopus 로고
    • The Solution of Initial Value Problems Using Interval Arithmetic
    • Stichting Mathematisch Centrum, Amsterdam
    • Eijgenraam P. The Solution of Initial Value Problems Using Interval Arithmetic. Mathematical Centre Tracts vol. 144 (1981), Stichting Mathematisch Centrum, Amsterdam
    • (1981) Mathematical Centre Tracts , vol.144
    • Eijgenraam, P.1
  • 7
    • 0344464829 scopus 로고    scopus 로고
    • A constraint satisfaction approach for enclosing solutions to parametric ordinary differential equations
    • Janssen M., Hentenryck P.V., and Deville Y. A constraint satisfaction approach for enclosing solutions to parametric ordinary differential equations. SIAM J. Numer. Anal. 40 (2002) 1896-1939
    • (2002) SIAM J. Numer. Anal. , vol.40 , pp. 1896-1939
    • Janssen, M.1    Hentenryck, P.V.2    Deville, Y.3
  • 10
    • 34547206345 scopus 로고    scopus 로고
    • Y. Lin, M.A. Stadtherr, Deterministic global optimization for parameter estimation of dynamic systems, Ind. Eng. Chem. Res., in press
  • 11
    • 34547208948 scopus 로고    scopus 로고
    • Y. Lin, M.A. Stadtherr, Guaranteed nonlinear state and parameter estimation for continuous-time systems, Automatica, submitted for publication
  • 12
    • 34547161638 scopus 로고    scopus 로고
    • Y. Lin, M.A. Stadtherr, Deterministic global optimization of nonlinear dynamic systems, AIChE J., in press
  • 13
    • 34547141425 scopus 로고    scopus 로고
    • Validated solution of ODEs with parametric uncertainties
    • Lin Y., and Stadtherr M.A. Validated solution of ODEs with parametric uncertainties. Computer-Aided Chem. Engrg. 21 (2006) 167-172
    • (2006) Computer-Aided Chem. Engrg. , vol.21 , pp. 167-172
    • Lin, Y.1    Stadtherr, M.A.2
  • 14
    • 46449129712 scopus 로고    scopus 로고
    • Y. Lin, M.A. Stadtherr, Fault detection in continuous-time systems with uncertain parameters, in: American Control Conference, New York, NY, 2007, submitted for publication
  • 15
    • 0000466527 scopus 로고
    • Enclosing the solutions of ordinary initial and boundary value problems
    • Kaucher C.U.E., and Kulisch U. (Eds), Teubner, Stuttgart
    • Lohner R.J. Enclosing the solutions of ordinary initial and boundary value problems. In: Kaucher C.U.E., and Kulisch U. (Eds). Computer Arithmetic: Scientific Computation and Programming Languages (1987), Teubner, Stuttgart
    • (1987) Computer Arithmetic: Scientific Computation and Programming Languages
    • Lohner, R.J.1
  • 16
    • 34547210425 scopus 로고    scopus 로고
    • R.J. Lohner, Einschließung der Lösung gewöhnlicher Anfangs- und Randwertaugfgaben und Anwendungen, PhD thesis, Universität Karlsruhe, Karlsruhe, Germany, 1988
  • 17
    • 34547222730 scopus 로고    scopus 로고
    • R.J. Lohner, Step size and order control in the verified solution of IVP with ODE's, in: SciCADE'95 International Conference on Scientific Computation and Differential Equations, Stanford University, Stanford, CA, 1995
  • 18
    • 0000241853 scopus 로고
    • Deterministic non-periodic flow
    • Lorenz E.N. Deterministic non-periodic flow. J. Atmospheric Sci. 20 (1963) 130-141
    • (1963) J. Atmospheric Sci. , vol.20 , pp. 130-141
    • Lorenz, E.N.1
  • 19
    • 34547167211 scopus 로고    scopus 로고
    • K. Makino, Rigorous analysis of nonlinear motion in particle accelerators, PhD thesis, Michigan State University, East Lansing, MI, 1998
  • 20
    • 0002646206 scopus 로고    scopus 로고
    • Remainder differential algebras and their applications
    • Berz M., Bishof C., Corliss G., and Griewank A. (Eds), SIAM, Philadelphia, PA
    • Makino K., and Berz M. Remainder differential algebras and their applications. In: Berz M., Bishof C., Corliss G., and Griewank A. (Eds). Computational Differentiation: Techniques, Application, and Tools (1996), SIAM, Philadelphia, PA
    • (1996) Computational Differentiation: Techniques, Application, and Tools
    • Makino, K.1    Berz, M.2
  • 21
    • 0001847776 scopus 로고    scopus 로고
    • Efficient control of the dependency problem based on Taylor model methods
    • Makino K., and Berz M. Efficient control of the dependency problem based on Taylor model methods. Reliable Computing 5 (1999) 3-12
    • (1999) Reliable Computing , vol.5 , pp. 3-12
    • Makino, K.1    Berz, M.2
  • 22
    • 34547179581 scopus 로고    scopus 로고
    • K. Makino, M. Berz, Suppression of the wrapping effect by Taylor model-based validated integrators, Technical Report MSUHEP 40910, Michigan State University, Lansing, MI, 2003
  • 23
    • 0345371405 scopus 로고    scopus 로고
    • Taylor models and other validated functional inclusion methods
    • Makino K., and Berz M. Taylor models and other validated functional inclusion methods. Int. J. Pure Appl. Math. 4 (2003) 379-456
    • (2003) Int. J. Pure Appl. Math. , vol.4 , pp. 379-456
    • Makino, K.1    Berz, M.2
  • 24
    • 34547164713 scopus 로고    scopus 로고
    • K. Makino, M. Berz, Taylor model range bounding schemes, in: Third International Workshop on Taylor Methods, Miami Beach, 2004
  • 25
    • 0004293209 scopus 로고
    • Prentice-Hall, Englewood Cliffs, NJ
    • Moore R.E. Interval Analysis (1966), Prentice-Hall, Englewood Cliffs, NJ
    • (1966) Interval Analysis
    • Moore, R.E.1
  • 26
    • 34547163636 scopus 로고    scopus 로고
    • N.S. Nedialkov, Computing rigorous bounds on the solution of an initial value problems for an ordinary differential equation, PhD thesis, University of Toronto, Toronto, Canada, 1999
  • 27
    • 0036679644 scopus 로고    scopus 로고
    • Some recent advances in validated methods for IVPs for ODEs
    • Nedialkov N.S., and Jackson K.R. Some recent advances in validated methods for IVPs for ODEs. Appl. Numer. Math. 42 (2002) 269-284
    • (2002) Appl. Numer. Math. , vol.42 , pp. 269-284
    • Nedialkov, N.S.1    Jackson, K.R.2
  • 28
    • 0002265766 scopus 로고    scopus 로고
    • Validated solutions of initial value problems for ordinary differential equations
    • Nedialkov N.S., Jackson K.R., and Corliss G.F. Validated solutions of initial value problems for ordinary differential equations. Appl. Math. Comput. 105 (1999) 21-68
    • (1999) Appl. Math. Comput. , vol.105 , pp. 21-68
    • Nedialkov, N.S.1    Jackson, K.R.2    Corliss, G.F.3
  • 29
    • 0035724114 scopus 로고    scopus 로고
    • An effective high-order interval method for validating existence and uniqueness of the solution of an IVP for an ODE
    • Nedialkov N.S., Jackson K.R., and Pryce J.D. An effective high-order interval method for validating existence and uniqueness of the solution of an IVP for an ODE. Reliable Computing 7 (2001) 449-465
    • (2001) Reliable Computing , vol.7 , pp. 449-465
    • Nedialkov, N.S.1    Jackson, K.R.2    Pryce, J.D.3
  • 30
    • 34547143969 scopus 로고    scopus 로고
    • M. Neher, K.R. Jackson, N.S. Nedialkov, On Taylor model based integration of ODEs, Technical Report, Department of Computer Science, University of Toronto, Toronto, Canada, 2005
  • 32
    • 0037292825 scopus 로고    scopus 로고
    • Taylor forms-use and limits
    • Neumaier A. Taylor forms-use and limits. Reliable Computing 9 (2002) 43-79
    • (2002) Reliable Computing , vol.9 , pp. 43-79
    • Neumaier, A.1
  • 33
    • 17644369306 scopus 로고    scopus 로고
    • Taylor models and floating point arithmetic: proof that arithmetic operations are bounded in COSY
    • Revol N., Makino K., and Berz M. Taylor models and floating point arithmetic: proof that arithmetic operations are bounded in COSY. J. Logic Algebr. Progr. 64 (2005) 135-154
    • (2005) J. Logic Algebr. Progr. , vol.64 , pp. 135-154
    • Revol, N.1    Makino, K.2    Berz, M.3
  • 34
    • 34547180096 scopus 로고    scopus 로고
    • A.B. Singer, Global dynamic optimization, PhD thesis, Massachusetts Institute of Technology, Cambridge, MA, 2004
  • 35
    • 33751231736 scopus 로고    scopus 로고
    • Bounding the solutions of parameter dependent nonlinear ordinary differential equations
    • Singer A.B., and Barton P.I. Bounding the solutions of parameter dependent nonlinear ordinary differential equations. SIAM J. Sci. Comput. 27 (2006) 2167-2182
    • (2006) SIAM J. Sci. Comput. , vol.27 , pp. 2167-2182
    • Singer, A.B.1    Barton, P.I.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.