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Volumn 54, Issue 11-12, 2011, Pages 2602-2615

Uncertainty propagation or box propagation

Author keywords

Automatic differentiation; Freeware software; Taylor series method; Uncertainty propagation

Indexed keywords

AUTOMATIC DIFFERENTIATIONS; BASIC OPERATION; FREEWARE SOFTWARES; HIGH ORDER; MULTI VARIABLES; NUMERICAL INTEGRATION TECHNIQUES; TAYLOR COEFFICIENTS; UNCERTAINTY PROPAGATION;

EID: 80052638722     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mcm.2011.06.036     Document Type: Article
Times cited : (8)

References (29)
  • 1
    • 0002265766 scopus 로고    scopus 로고
    • Validated solutions of initial value problems for ordinary differential equations
    • Nedialkov N.S., Jackson K.R., Corliss G.F. Validated solutions of initial value problems for ordinary differential equations. Appl. Math. Comput. 1999, 105(1):21-68.
    • (1999) Appl. Math. Comput. , vol.105 , Issue.1 , pp. 21-68
    • Nedialkov, N.S.1    Jackson, K.R.2    Corliss, G.F.3
  • 4
    • 32844454596 scopus 로고    scopus 로고
    • Cosy infinity version 9, Nuclear Instruments and Methods in Physics Research Section A
    • Accelerators, Spectrometers, Detectors and Associated Equipment 558 (1) (2006) 346-350, Proceedings of the 8th International Computational Accelerator Physics Conference - ICAP
    • K. Makino, M. Berz, Cosy infinity version 9, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 558 (1) (2006) 346-350, Proceedings of the 8th International Computational Accelerator Physics Conference - ICAP 2004.
    • (2004)
    • Makino, K.1    Berz, M.2
  • 5
    • 0345371405 scopus 로고    scopus 로고
    • Taylor models and other validated functional inclusion methods
    • Makino K., Berz M. Taylor models and other validated functional inclusion methods. Int. J. Pure Appl. Math. 2003, 6(3):239-316.
    • (2003) Int. J. Pure Appl. Math. , vol.6 , Issue.3 , pp. 239-316
    • Makino, K.1    Berz, M.2
  • 6
    • 33845503029 scopus 로고    scopus 로고
    • Nonlinear mapping of Gaussian statistics: theory and applications to spacecraft trajectory design
    • Park R., Scheeres D. Nonlinear mapping of Gaussian statistics: theory and applications to spacecraft trajectory design. J. Guid. Control Dyn. 2006, 29(6):1367-1375.
    • (2006) J. Guid. Control Dyn. , vol.29 , Issue.6 , pp. 1367-1375
    • Park, R.1    Scheeres, D.2
  • 7
    • 58149488788 scopus 로고    scopus 로고
    • Application of high order expansions of two-point boundary value problems to astrodynamics
    • Di Lizia P., Armellin R., Lavagna M. Application of high order expansions of two-point boundary value problems to astrodynamics. Celestial Mech. Dynam. Astronom. 2008, 102(4):355-375.
    • (2008) Celestial Mech. Dynam. Astronom. , vol.102 , Issue.4 , pp. 355-375
    • Di Lizia, P.1    Armellin, R.2    Lavagna, M.3
  • 8
    • 80052638357 scopus 로고    scopus 로고
    • TIDES: a Taylor series integrator for differential equations
    • ACM Transactions on Mathematical Software (in press).
    • A. Abad, R. Barrio, F. Blesa, M. Rodríguez, TIDES: a Taylor series integrator for differential equations, ACM Transactions on Mathematical Software (2011) (in press).
    • (2011)
    • Abad, A.1    Barrio, R.2    Blesa, F.3    Rodríguez, M.4
  • 9
    • 0004149831 scopus 로고    scopus 로고
    • Wolfram Media, Inc., Champaign, IL
    • Wolfram S. The Mathematica® Book 1999, Wolfram Media, Inc., Champaign, IL. 4th ed.
    • (1999) The Mathematica® Book
    • Wolfram, S.1
  • 10
    • 17944378468 scopus 로고    scopus 로고
    • Ordinary Differential Equations
    • SIAM, Philadelphia, PA
    • Hartman P. Ordinary Differential Equations. Classics in Applied Mathematics 2002, vol. 38. SIAM, Philadelphia, PA.
    • (2002) Classics in Applied Mathematics , vol.38
    • Hartman, P.1
  • 11
    • 33751249935 scopus 로고    scopus 로고
    • Sensitivity analysis of ODEs/DAEs using the Taylor series method
    • Barrio R. Sensitivity analysis of ODEs/DAEs using the Taylor series method. SIAM J. Sci. Comput. 2006, 27(6):1929-1947.
    • (2006) SIAM J. Sci. Comput. , vol.27 , Issue.6 , pp. 1929-1947
    • Barrio, R.1
  • 12
  • 13
    • 0020143282 scopus 로고
    • Solving ordinary differential equations using Taylor series
    • Corliss G., Chang Y.F. Solving ordinary differential equations using Taylor series. ACM Trans. Math. Software 1982, 8(2):114-144.
    • (1982) ACM Trans. Math. Software , vol.8 , Issue.2 , pp. 114-144
    • Corliss, G.1    Chang, Y.F.2
  • 14
    • 13544262350 scopus 로고    scopus 로고
    • Performance of the Taylor series method for ODEs/DAEs
    • Barrio R. Performance of the Taylor series method for ODEs/DAEs. Appl. Math. Comput. 2005, 163(2):525-545.
    • (2005) Appl. Math. Comput. , vol.163 , Issue.2 , pp. 525-545
    • Barrio, R.1
  • 15
    • 27544484059 scopus 로고    scopus 로고
    • VSVO formulation of the Taylor method for the numerical solution of ODEs
    • Barrio R., Blesa F., Lara M. VSVO formulation of the Taylor method for the numerical solution of ODEs. Comput. Math. Appl. 2005, 50(1-2):93-111.
    • (2005) Comput. Math. Appl. , vol.50 , Issue.1-2 , pp. 93-111
    • Barrio, R.1    Blesa, F.2    Lara, M.3
  • 17
    • 0040763312 scopus 로고
    • ATOMFT: solving ODEs and DAEs using Taylor series
    • Chang Y.F., Corliss G. ATOMFT: solving ODEs and DAEs using Taylor series. Comput. Math. Appl. 1994, 28(10-12):209-233.
    • (1994) Comput. Math. Appl. , vol.28 , Issue.10-12 , pp. 209-233
    • Chang, Y.F.1    Corliss, G.2
  • 18
    • 22544468094 scopus 로고    scopus 로고
    • A software package for the numerical integration of ODEs by means of high-order Taylor methods
    • Jorba Á, Zou M. A software package for the numerical integration of ODEs by means of high-order Taylor methods. Experiment. Math. 2005, 14(1):99-117.
    • (2005) Experiment. Math. , vol.14 , Issue.1 , pp. 99-117
    • Jorba Á1    Zou, M.2
  • 19
    • 0002402664 scopus 로고
    • Algorithms for higher derivatives in many variables with applications to beam physics
    • SIAM, Philadelphia, PA
    • Berz M. Algorithms for higher derivatives in many variables with applications to beam physics. Automatic Differentiation of Algorithms 1991, 147-156. SIAM, Philadelphia, PA.
    • (1991) Automatic Differentiation of Algorithms , pp. 147-156
    • Berz, M.1
  • 20
    • 34047210346 scopus 로고    scopus 로고
    • Validated solutions of initial value problems for parametric odes
    • Lin Y., Stadtherr M.A. Validated solutions of initial value problems for parametric odes. Appl. Numer. Math. 2007, 57(10):1145-1162.
    • (2007) Appl. Numer. Math. , vol.57 , Issue.10 , pp. 1145-1162
    • Lin, Y.1    Stadtherr, M.A.2
  • 22
    • 0000329979 scopus 로고    scopus 로고
    • Verified integration of ODEs and flows using differential algebraic methods on high-order Taylor models
    • Berz M., Makino K. Verified integration of ODEs and flows using differential algebraic methods on high-order Taylor models. Reliab. Comput. 1998, 4(4):361-369.
    • (1998) Reliab. Comput. , vol.4 , Issue.4 , pp. 361-369
    • Berz, M.1    Makino, K.2
  • 23
    • 0002249579 scopus 로고    scopus 로고
    • An introduction to automatic differentiation
    • SIAM, Philadelphia, PA
    • Rall L.B., Corliss G.F. An introduction to automatic differentiation. Computational Differentiation 1996, 1-18. SIAM, Philadelphia, PA.
    • (1996) Computational Differentiation , pp. 1-18
    • Rall, L.B.1    Corliss, G.F.2
  • 24
    • 0004293209 scopus 로고
    • Prentice-Hall Inc., Englewood Cliffs, N.J.
    • Moore R.E. Interval Analysis 1966, Prentice-Hall Inc., Englewood Cliffs, N.J.
    • (1966) Interval Analysis
    • Moore, R.E.1
  • 25
    • 0000241853 scopus 로고
    • Deterministic nonperiodic flow
    • Lorenz E. Deterministic nonperiodic flow. J. Atmospheric Sci. 1963, 20:130-141.
    • (1963) J. Atmospheric Sci. , vol.20 , pp. 130-141
    • Lorenz, E.1
  • 28
    • 34247637165 scopus 로고    scopus 로고
    • A three-parametric study of the Lorenz model
    • Barrio R., Serrano S A three-parametric study of the Lorenz model. Physica D 2007, 229(1):43-51.
    • (2007) Physica D , vol.229 , Issue.1 , pp. 43-51
    • Barrio, R.1    Serrano, S.2
  • 29
    • 67650069838 scopus 로고    scopus 로고
    • Bounds for the chaotic region in the Lorenz model
    • Barrio R., Serrano S. Bounds for the chaotic region in the Lorenz model. Physica D 2009, 238(1):1615-1624.
    • (2009) Physica D , vol.238 , Issue.1 , pp. 1615-1624
    • Barrio, R.1    Serrano, S.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.