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Volumn 26, Issue 2, 2001, Pages 131-150

Variable stepsize schemes for effective order methods and enhanced order composition methods

Author keywords

Composition methods; Effective order; Principal local truncation error; The C and D simplifying assumptions; The Picard integral

Indexed keywords


EID: 0035594228     PISSN: 10171398     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1016628315914     Document Type: Article
Times cited : (3)

References (16)
  • 1
    • 0002612111 scopus 로고
    • A special family of Runge-Kutta methods for solving stiff differential equations
    • K. Burrage, A special family of Runge-Kutta methods for solving stiff differential equations, BIT 18 (1978) 22-41.
    • (1978) BIT , vol.18 , pp. 22-41
    • Burrage, K.1
  • 3
    • 84968481790 scopus 로고
    • An algebraic theory of integration methods
    • J.C. Butcher, An algebraic theory of integration methods, Math. Comp. 26 (1972) 79-106.
    • (1972) Math. Comp. , vol.26 , pp. 79-106
    • Butcher, J.C.1
  • 5
    • 0025448875 scopus 로고
    • Towards efficient Runge-Kutta methods for stiff systems
    • J.C. Butcher and J.R. Cash, Towards efficient Runge-Kutta methods for stiff systems, SIAM J. Numer. Anal. 27 (1990) 753-761.
    • (1990) SIAM J. Numer. Anal. , vol.27 , pp. 753-761
    • Butcher, J.C.1    Cash, J.R.2
  • 6
    • 0034230353 scopus 로고    scopus 로고
    • Multi-step zero approximation for stepsize control
    • J.C. Butcher and T.M.H. Chan, Multi-step zero approximation for stepsize control, Appl. Numer. Math. 34 (2000) 167-177.
    • (2000) Appl. Numer. Math. , vol.34 , pp. 167-177
    • Butcher, J.C.1    Chan, T.M.H.2
  • 7
    • 0041728458 scopus 로고    scopus 로고
    • The effective order of singly-implicit Runge-Kutta methods
    • Preprint
    • J.C. Butcher and P. Chartier, The effective order of singly-implicit Runge-Kutta methods, Preprint, Appl. Numer. Math. (1999).
    • (1999) Appl. Numer. Math.
    • Butcher, J.C.1    Chartier, P.2
  • 8
    • 0032182591 scopus 로고    scopus 로고
    • ESIRK methods and variable stepsize
    • J.C. Butcher and D.J.L. Chen, ESIRK methods and variable stepsize, Appl. Numer. Math. 28 (1998) 193-207.
    • (1998) Appl. Numer. Math. , vol.28 , pp. 193-207
    • Butcher, J.C.1    Chen, D.J.L.2
  • 9
    • 0032388654 scopus 로고    scopus 로고
    • Diagonally extended simply implicit Runge-Kutta effective methods
    • J.C. Butcher and M.T. Diamantakis, Diagonally extended simply implicit Runge-Kutta effective methods, Numer. Algorithms 17 (1998) 121-145.
    • (1998) Numer. Algorithms , vol.17 , pp. 121-145
    • Butcher, J.C.1    Diamantakis, M.T.2
  • 10
    • 0030283844 scopus 로고    scopus 로고
    • The number of conditions for a Runge-Kutta method to have effective order p, Special Issue Celebrating the Centenary of Runge-Kutta methods
    • J.C. Butcher and J.M. Sanz-Serna, The number of conditions for a Runge-Kutta method to have effective order p, Special Issue Celebrating the Centenary of Runge-Kutta methods, Appl. Numer. Math. 22(1-3) (1996) 103-111.
    • (1996) Appl. Numer. Math. , vol.22 , Issue.1-3 , pp. 103-111
    • Butcher, J.C.1    Sanz-Serna, J.M.2
  • 12
    • 0015022401 scopus 로고
    • Cyclic composite multistep predictor-corrector methods
    • J. Donelson and E. Hansen, Cyclic composite multistep predictor-corrector methods, SIAM J. Numer. Anal. 8 (1971) 137-157.
    • (1971) SIAM J. Numer. Anal. , vol.8 , pp. 137-157
    • Donelson, J.1    Hansen, E.2
  • 14
    • 0015960381 scopus 로고
    • On the Butcher group and general multi-value methods
    • E. Hairer and G. Wanner, On the Butcher group and general multi-value methods, Computing (Arch. Elektron. Rechnen) 13(1) (1974) 1-15.
    • (1974) Computing (Arch. Elektron. Rechnen) , vol.13 , Issue.1 , pp. 1-15
    • Hairer, E.1    Wanner, G.2
  • 15
    • 0015484437 scopus 로고
    • Comparing numerical methods for ordinary differential equations
    • errata, ibid. 11 (1974) 681
    • T.E. Hull, W.H. Enright, B.M. Fellen and A.E. Sedgwick, Comparing numerical methods for ordinary differential equations, SIAM J. Numer. Anal. 9 (1972) 603-637; errata, ibid. 11 (1974) 681.
    • (1972) SIAM J. Numer. Anal. , vol.9 , pp. 603-637
    • Hull, T.E.1    Enright, W.H.2    Fellen, B.M.3    Sedgwick, A.E.4
  • 16
    • 0009559049 scopus 로고
    • Cheap enhancement of symplectic integrators
    • Numerical Analysis 1995, Dundee, Longman, Harlow
    • M.A. López-Marcos, J.M. Sanz-Serna and R.D. Skeel, Cheap enhancement of symplectic integrators, in: Numerical Analysis 1995, Dundee, 1995, Pitman Research Notes Math. Series, Vol. 344 (Longman, Harlow, 1996) pp. 107-122.
    • (1995) Pitman Research Notes Math. Series , vol.344 , pp. 107-122
    • López-Marcos, M.A.1    Sanz-Serna, J.M.2    Skeel, R.D.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.