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Volumn 40, Issue 2, 2000, Pages 314-335

Dynamical systems and adaptive timestepping in ODE solvers

Author keywords

Error control; Numerical integration; Ordinary differential equations

Indexed keywords


EID: 0042185225     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022395124683     Document Type: Article
Times cited : (15)

References (17)
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    • A PI-stepsize control for the numerical solution of ordinary differential equations
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    • Gustafsson, K.1    Lundh, M.2    Söderlind, G.3
  • 6
    • 84948497651 scopus 로고
    • Upper semicontinuity of attractors for approximations of semigroups and partial differential equations
    • J. Hale, X. Lin, and G. Raugel, Upper semicontinuity of attractors for approximations of semigroups and partial differential equations, Math. Comp., 50 (1988), pp. 89-123.
    • (1988) Math. Comp. , vol.50 , pp. 89-123
    • Hale, J.1    Lin, X.2    Raugel, G.3
  • 7
    • 0022129420 scopus 로고
    • Equilibrium states of Runge-Kutta schemes
    • G. Hall, Equilibrium states of Runge-Kutta schemes, ACM Trans. Math. Software, 11 (1985), pp. 289-301.
    • (1985) ACM Trans. Math. Software , vol.11 , pp. 289-301
    • Hall, G.1
  • 9
    • 0000649975 scopus 로고
    • Stable attracting sets in dynamical systems and their one-step discretizations
    • P. Kloeden and J. Lorenz, Stable attracting sets in dynamical systems and their one-step discretizations, SIAM J. Num. Anal., 23 (1986), pp. 986-995.
    • (1986) SIAM J. Num. Anal. , vol.23 , pp. 986-995
    • Kloeden, P.1    Lorenz, J.2
  • 10
    • 0041723519 scopus 로고    scopus 로고
    • Convergence results for the MATLAB ode23 routine
    • H. Lamba and A. Stuart, Convergence results for the MATLAB ode23 routine, BIT, 38 (1998), pp. 751-780.
    • (1998) BIT , vol.38 , pp. 751-780
    • Lamba, H.1    Stuart, A.2
  • 13
    • 0041723517 scopus 로고
    • Considerations concerning a theory for ODE solvers
    • Numerical Treatment of Differential Equations, Springer-Verlag, Berlin
    • H. Stetter, Considerations concerning a theory for ODE solvers, in Numerical Treatment of Differential Equations, Lecture Notes in Mathematics, 631, Springer-Verlag, Berlin, 1976.
    • (1976) Lecture Notes in Mathematics , vol.631
    • Stetter, H.1
  • 15
    • 0000180095 scopus 로고
    • Invariant curves for variable step size integrators
    • D. Stoffer and K. Nipp, Invariant curves for variable step size integrators, BIT, 31 (1991), pp. 169-180.
    • (1991) BIT , vol.31 , pp. 169-180
    • Stoffer, D.1    Nipp, K.2
  • 16
    • 0031527059 scopus 로고    scopus 로고
    • Probabilistic and deterministic convergence proofs for software for initial value problems
    • A. Stuart, Probabilistic and deterministic convergence proofs for software for initial value problems, Numerical Algorithms, 14 (1997), pp. 227-260.
    • (1997) Numerical Algorithms , vol.14 , pp. 227-260
    • Stuart, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.