메뉴 건너뛰기




Volumn 33, Issue 1, 2007, Pages

Robust and reliable defect control for Runge-Kutta methods

Author keywords

Initial value problems; Interpolation; Ordinary differential equations; Runge Kutta methods

Indexed keywords

FLOATING-POINT METHODS; INTERVAL-BASED METHODS; RELIABILITY SPECTRUM;

EID: 33947702166     PISSN: 00983500     EISSN: 15577295     Source Type: Journal    
DOI: 10.1145/1206040.1206041     Document Type: Article
Times cited : (19)

References (14)
  • 1
    • 0004859370 scopus 로고
    • Error Backward
    • CORLESS, R. M. 1994. Error Backward. Contemp. Math. 172, 31-62.
    • (1994) Contemp. Math , vol.172 , pp. 31-62
    • CORLESS, R.M.1
  • 3
    • 0010965403 scopus 로고
    • Analysis of error control stategies for continuous Runge-Kutta methods
    • ENRIGHT, W. H. 1989a. Analysis of error control stategies for continuous Runge-Kutta methods. SIAM J. Numer. Analys. 26, 3, 588-599.
    • (1989) SIAM J. Numer. Analys , vol.26 , Issue.3 , pp. 588-599
    • ENRIGHT, W.H.1
  • 4
    • 0001743435 scopus 로고
    • A new error-control for initial value solvers
    • ENRIGHT, W. H. 1989b. A new error-control for initial value solvers. Appl. Math. Comp. 31, 288-301.
    • (1989) Appl. Math. Comp , vol.31 , pp. 288-301
    • ENRIGHT, W.H.1
  • 5
    • 0027684529 scopus 로고
    • The relative efficiency of alternative defect control schemes for high-order continuous Runge-Kutta formulas
    • ENRIGHT, W. H. 1993. The relative efficiency of alternative defect control schemes for high-order continuous Runge-Kutta formulas. SIAM J. Numer. Analys. 30, 5, 1419-1445.
    • (1993) SIAM J. Numer. Analys , vol.30 , Issue.5 , pp. 1419-1445
    • ENRIGHT, W.H.1
  • 6
    • 0040278315 scopus 로고
    • Parallel defect control
    • ENRIGHT, W. H. AND HIGHAM, D. J. 1991. Parallel defect control. BIT 31, 647-663.
    • (1991) BIT 31 , pp. 647-663
    • ENRIGHT, W.H.1    HIGHAM, D.J.2
  • 8
    • 2642533176 scopus 로고    scopus 로고
    • Ph.D. dissertation. Department of Computer Science, University of Toronto, Toronto, Ont, Canada. Available on the Web as
    • HAYES, W. B. 2001. Rigorous Shadowing of Numerical Solutions of Ordinary Differential Equations by Containment. Ph.D. dissertation. Department of Computer Science, University of Toronto, Toronto, Ont., Canada. Available on the Web as http://www.cs.toronto.edu/NA/reports.html#hayes-01-phd.
    • (2001) Rigorous Shadowing of Numerical Solutions of Ordinary Differential Equations by Containment
    • HAYES, W.B.1
  • 9
    • 0005691331 scopus 로고
    • Robust defect control with Runge-Kutta schemes
    • HIGHAM, D. J. 1989. Robust defect control with Runge-Kutta schemes. SIAM J. Numer. Analys. 26, 5, 1175-1183.
    • (1989) SIAM J. Numer. Analys , vol.26 , Issue.5 , pp. 1175-1183
    • HIGHAM, D.J.1
  • 11
    • 33947659078 scopus 로고    scopus 로고
    • HULL, T. E., ENRIGHT, W. H., AND JACKSON, K. R. 1986. User's guide for DVERK - a subroutine for solving non-stiff ODEs. Tech. Rep. UT-DCS-100. Department of Computer Science, University of Toronto. Source code available from the authors, or online from http //www.netlib.org/ in the ODE directory.
    • HULL, T. E., ENRIGHT, W. H., AND JACKSON, K. R. 1986. User's guide for DVERK - a subroutine for solving non-stiff ODEs. Tech. Rep. UT-DCS-100. Department of Computer Science, University of Toronto. Source code available from the authors, or online from http //www.netlib.org/ in the ODE directory.
  • 12
    • 0023312263 scopus 로고
    • Two FORTRAN packages for assessing initial value methods
    • PRYCE, J. AND ENRIGHT, W. 1987. Two FORTRAN packages for assessing initial value methods. ACM Trans. Math. Softw. 13, 1-27.
    • (1987) ACM Trans. Math. Softw , vol.13 , pp. 1-27
    • PRYCE, J.1    ENRIGHT, W.2
  • 13
    • 33947633626 scopus 로고    scopus 로고
    • STETTER, H. J. 1978. Considerations concerning a theory for ODE-solvers. In Numerical Treatment of Differential Equations (Proc. Oberwolfach 1976). Lecture Notes in Mathematics, 631. Springer, Berlin/Heidelberg, Germany, 188-200.
    • STETTER, H. J. 1978. Considerations concerning a theory for ODE-solvers. In Numerical Treatment of Differential Equations (Proc. Oberwolfach 1976). Lecture Notes in Mathematics, vol. 631. Springer, Berlin/Heidelberg, Germany, 188-200.
  • 14
    • 0027683528 scopus 로고
    • Differentiable interpolants for high-order Runge-Kutta methods
    • VERNER, J. H. 1993. Differentiable interpolants for high-order Runge-Kutta methods. SIAM J. Numer. Analys. 30, 5, 1446-1466.
    • (1993) SIAM J. Numer. Analys , vol.30 , Issue.5 , pp. 1446-1466
    • VERNER, J.H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.