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Volumn 14, Issue 1-3, 1997, Pages 227-260

Probabilistic and deterministic convergence proofs for software for initial value problems

Author keywords

Convergence; Error control

Indexed keywords


EID: 0031527059     PISSN: 10171398     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1019169114976     Document Type: Article
Times cited : (8)

References (16)
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    • Demmel, J.W.1
  • 5
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    • (1992) Math. Comp. , vol.58 , pp. 185-190
    • Edelman, A.1
  • 6
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    • (1985) ACM Trans, on Math. Software , vol.11 , pp. 289-301
    • Hall, G.1
  • 7
    • 0012211602 scopus 로고
    • Global error versus tolerance for explicit Runge-Kutta methods
    • D. J. Higham, Global error versus tolerance for explicit Runge-Kutta methods, IMA J. Numer. Anal. 11 (1991) 457-480
    • (1991) IMA J. Numer. Anal. , vol.11 , pp. 457-480
    • Higham, D.J.1
  • 8
    • 0000429790 scopus 로고
    • Average-case stability of gaussian elimination
    • R. Schrieber and L. N. Trefethen, Average-case stability of gaussian elimination, SIAM J. Matrix Anal. 11 (1990) 335-360.
    • (1990) SIAM J. Matrix Anal. , vol.11 , pp. 335-360
    • Schrieber, R.1    Trefethen, L.N.2
  • 9
    • 14844326245 scopus 로고
    • Tolerance proportionality in ODE codes
    • eds. A. Bellen, C. Gear and E. Russo, Lecture Notes in Mathematics Springer, Berlin
    • L. F. Shampine, Tolerance proportionality in ODE codes, in: Numerical Methods for Ordinary Differential Equations (Proceedings), eds. A. Bellen, C. Gear and E. Russo, Lecture Notes in Mathematics 1386 (Springer, Berlin, 1987) pp. 118-136.
    • (1987) Numerical Methods for Ordinary Differential Equations (Proceedings) , vol.1386 , pp. 118-136
    • Shampine, L.F.1
  • 10
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    • The fundamental theorem of algebra and complexity theory
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    • (1981) Bull. Amer. Math. Soc. , vol.4 , pp. 1-35
    • Smale, S.1
  • 11
    • 0041527287 scopus 로고
    • Considerations concerning s theory for ODE-solvers
    • eds. R. Burlisch, R. Grigorieff and J. Schröder, Lecture Notes in Mathematics Springer, Berlin
    • H. J. Stetter, Considerations concerning s theory for ODE-solvers, in: Numerical Treatment of Differential Equations, eds. R. Burlisch, R. Grigorieff and J. Schröder, Lecture Notes in Mathematics 631 (Springer, Berlin, 1976).
    • (1976) Numerical Treatment of Differential Equations , vol.631
    • Stetter, H.J.1
  • 13
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    • Invariant curves for variable step-size integrators
    • D. Stoffer and K. Nipp, Invariant curves for variable step-size integrators, BIT 31 (1991) 169-180 and BIT 32 (1992) 367-368.
    • (1991) BIT , vol.31 , pp. 169-180
    • Stoffer, D.1    Nipp, K.2
  • 14
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    • D. Stoffer and K. Nipp, Invariant curves for variable step-size integrators, BIT 31 (1991) 169-180 and BIT 32 (1992) 367-368.
    • (1992) BIT , vol.32 , pp. 367-368


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.