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Volumn 53, Issue 2-4, 2005, Pages 149-163

Nordsieck representation of two-step Runge-Kutta methods for ordinary differential equations

Author keywords

Error estimation and control; Error propagation; Nordsieck representation; Two step Runge Kutta methods

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; ERROR ANALYSIS; ORDINARY DIFFERENTIAL EQUATIONS; SET THEORY; VECTORS;

EID: 14844325318     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2004.08.010     Document Type: Conference Paper
Times cited : (20)

References (39)
  • 1
    • 0032344798 scopus 로고    scopus 로고
    • Construction of two-step Runge-Kutta methods of high order for ordinary differential equations
    • Z. Bartoszewski, and Z. Jackiewicz Construction of two-step Runge-Kutta methods of high order for ordinary differential equations Numer. Algorithms 18 1998 51 70
    • (1998) Numer. Algorithms , vol.18 , pp. 51-70
    • Bartoszewski, Z.1    Jackiewicz, Z.2
  • 2
    • 0041338081 scopus 로고    scopus 로고
    • Toward a two-step Runge-Kutta code for nonstiff differential equations
    • Z. Bartoszewski, and Z. Jackiewicz Toward a two-step Runge-Kutta code for nonstiff differential equations Appl. Math. 28 2001 353 365
    • (2001) Appl. Math. , vol.28 , pp. 353-365
    • Bartoszewski, Z.1    Jackiewicz, Z.2
  • 3
    • 0036630251 scopus 로고    scopus 로고
    • Stability analysis of two-step Runge-Kutta methods for delay differential equations
    • Z. Bartoszewski, and Z. Jackiewicz Stability analysis of two-step Runge-Kutta methods for delay differential equations Comput. Math. Appl. 44 2002 83 93
    • (2002) Comput. Math. Appl. , vol.44 , pp. 83-93
    • Bartoszewski, Z.1    Jackiewicz, Z.2
  • 6
    • 0000452884 scopus 로고    scopus 로고
    • Implementation of diagonally implicit multistage integration methods for ordinary differential equations
    • J.C. Butcher, and Z. Jackiewicz Implementation of diagonally implicit multistage integration methods for ordinary differential equations SIAM J. Numer. Anal. 34 1997 2119 2141
    • (1997) SIAM J. Numer. Anal. , vol.34 , pp. 2119-2141
    • Butcher, J.C.1    Jackiewicz, Z.2
  • 7
    • 0042318570 scopus 로고    scopus 로고
    • A reliable error estimation for diagonally implicit multistage integration methods
    • J.C. Butcher, and Z. Jackiewicz A reliable error estimation for diagonally implicit multistage integration methods BIT 41 2001 656 665
    • (2001) BIT , vol.41 , pp. 656-665
    • Butcher, J.C.1    Jackiewicz, Z.2
  • 8
    • 0036441464 scopus 로고    scopus 로고
    • Error estimation for Nordsieck methods
    • J.C. Butcher, and Z. Jackiewicz Error estimation for Nordsieck methods Numer. Algorithms 31 2002 75 85
    • (2002) Numer. Algorithms , vol.31 , pp. 75-85
    • Butcher, J.C.1    Jackiewicz, Z.2
  • 9
    • 0345060035 scopus 로고    scopus 로고
    • A new approach to error estimation for general linear methods
    • J.C. Butcher, and Z. Jackiewicz A new approach to error estimation for general linear methods Numer. Math. 95 2003 487 502
    • (2003) Numer. Math. , vol.95 , pp. 487-502
    • Butcher, J.C.1    Jackiewicz, Z.2
  • 10
    • 0031212298 scopus 로고    scopus 로고
    • Order conditions for two-step Runge-Kutta methods
    • J.C. Butcher, and S. Tracogna Order conditions for two-step Runge-Kutta methods Appl. Numer. Math. 24 1997 351 364
    • (1997) Appl. Numer. Math. , vol.24 , pp. 351-364
    • Butcher, J.C.1    Tracogna, S.2
  • 11
    • 0005366895 scopus 로고
    • Pseudo-Runge-Kutta methods involving two points
    • G.D. Byrne, and R.J. Lambert Pseudo-Runge-Kutta methods involving two points J. Assoc. Comput. Mach. 13 1966 114 123
    • (1966) J. Assoc. Comput. Mach. , vol.13 , pp. 114-123
    • Byrne, G.D.1    Lambert, R.J.2
  • 12
    • 0042121057 scopus 로고    scopus 로고
    • Construction of two-step Runge-Kutta methods with large regions of absolute stability
    • J. Chollom, and Z. Jackiewicz Construction of two-step Runge-Kutta methods with large regions of absolute stability J. Comput. Appl. Math. 157 2003 125 137
    • (2003) J. Comput. Appl. Math. , vol.157 , pp. 125-137
    • Chollom, J.1    Jackiewicz, Z.2
  • 15
    • 0005297545 scopus 로고    scopus 로고
    • Order conditions for general two-step Runge-Kutta methods
    • E. Hairer, and G. Wanner Order conditions for general two-step Runge-Kutta methods SIAM J. Numer. Anal. 34 1997 2087 2089
    • (1997) SIAM J. Numer. Anal. , vol.34 , pp. 2087-2089
    • Hairer, E.1    Wanner, G.2
  • 16
    • 38249001338 scopus 로고
    • The tolerance proportionality of adaptive ODE solvers
    • D.J. Higham The tolerance proportionality of adaptive ODE solvers J. Comput. Appl. Math. 45 1993 227 236
    • (1993) J. Comput. Appl. Math. , vol.45 , pp. 227-236
    • Higham, D.J.1
  • 19
    • 0001164459 scopus 로고
    • A general class of two-step Runge-Kutta methods for ordinary differential equations
    • Z. Jackiewicz, and S. Tracogna A general class of two-step Runge-Kutta methods for ordinary differential equations SIAM J. Numer. Anal. 32 1995 1390 1427
    • (1995) SIAM J. Numer. Anal. , vol.32 , pp. 1390-1427
    • Jackiewicz, Z.1    Tracogna, S.2
  • 21
    • 21344471075 scopus 로고    scopus 로고
    • Variable stepsize continuous two-step Runge-Kutta methods for ordinary differential equations
    • Z. Jackiewicz, and S. Tracogna Variable stepsize continuous two-step Runge-Kutta methods for ordinary differential equations Numer. Algorithms 12 1996 347 368
    • (1996) Numer. Algorithms , vol.12 , pp. 347-368
    • Jackiewicz, Z.1    Tracogna, S.2
  • 22
    • 0001472260 scopus 로고    scopus 로고
    • General linear methods with external stages of different orders
    • Z. Jackiewicz, and R. Vermiglio General linear methods with external stages of different orders BIT 36 1996 688 712
    • (1996) BIT , vol.36 , pp. 688-712
    • Jackiewicz, Z.1    Vermiglio, R.2
  • 23
    • 0042840802 scopus 로고    scopus 로고
    • Derivation and implementation of two-step Runge-Kutta pairs
    • Z. Jackiewicz, and J.H. Verner Derivation and implementation of two-step Runge-Kutta pairs Japan J. Indust. Appl. Math. 19 2002 227 248
    • (2002) Japan J. Indust. Appl. Math. , vol.19 , pp. 227-248
    • Jackiewicz, Z.1    Verner, J.H.2
  • 24
    • 84968518141 scopus 로고
    • Variable-stepsize explicit two-step Runge-Kutta methods
    • Z. Jackiewicz, and M. Zennaro Variable-stepsize explicit two-step Runge-Kutta methods Math. Comp. 59 1992 421 438
    • (1992) Math. Comp. , vol.59 , pp. 421-438
    • Jackiewicz, Z.1    Zennaro, M.2
  • 27
    • 84966199026 scopus 로고
    • Order barriers for continuous explicit Runge-Kutta methods
    • B. Owren, and M. Zennaro Order barriers for continuous explicit Runge-Kutta methods Math. Comp. 56 1991 645 661
    • (1991) Math. Comp. , vol.56 , pp. 645-661
    • Owren, B.1    Zennaro, M.2
  • 28
    • 0043242780 scopus 로고
    • Derivation of efficient, continuous, explicit Runge-Kutta methods
    • B. Owren, and M. Zennaro Derivation of efficient, continuous, explicit Runge-Kutta methods SIAM J. Sci. Statist. Comput. 13 1992 1488 1501
    • (1992) SIAM J. Sci. Statist. Comput. , vol.13 , pp. 1488-1501
    • Owren, B.1    Zennaro, M.2
  • 29
    • 84966250956 scopus 로고
    • Two-step Runge-Kutta methods and hyperbolic partial differential equations
    • R.A. Renaut Two-step Runge-Kutta methods and hyperbolic partial differential equations Math. Comp. 55 1990 563 579
    • (1990) Math. Comp. , vol.55 , pp. 563-579
    • Renaut, R.A.1
  • 30
    • 0021777240 scopus 로고
    • The step sizes used by one-step codes for ODEs
    • L.F. Shampine The step sizes used by one-step codes for ODEs Appl. Numer. Math. 1 1985 95 106
    • (1985) Appl. Numer. Math. , vol.1 , pp. 95-106
    • Shampine, L.F.1
  • 31
    • 14844326245 scopus 로고
    • Tolerance proportionality in ODE codes
    • A. Bellen C.W. Gear E. Russo, Numerical Methods for Ordinary Differential Equations, Springer Berlin
    • L.F. Shampine Tolerance proportionality in ODE codes A. Bellen C.W. Gear E. Russo Numerical Methods for Ordinary Differential Equations Lecture Notes in Mathematics vol. 1386 1989 Springer Berlin 118 136
    • (1989) Lecture Notes in Mathematics , vol.1386 , pp. 118-136
    • Shampine, L.F.1
  • 34
    • 0030400404 scopus 로고    scopus 로고
    • Implementation of two-step Runge-Kutta methods for ordinary differential equations
    • S. Tracogna Implementation of two-step Runge-Kutta methods for ordinary differential equations J. Comput. Appl. Math. 76 1997 113 136
    • (1997) J. Comput. Appl. Math. , vol.76 , pp. 113-136
    • Tracogna, S.1
  • 35
    • 0005292548 scopus 로고    scopus 로고
    • Two-step Runge-Kutta: Theory and practice
    • S. Tracogna, and B. Welfert Two-step Runge-Kutta: Theory and practice BIT 40 2000 775 799
    • (2000) BIT , vol.40 , pp. 775-799
    • Tracogna, S.1    Welfert, B.2
  • 38
    • 84966233444 scopus 로고
    • Natural continuous extensions of Runge-Kutta methods
    • M. Zennaro Natural continuous extensions of Runge-Kutta methods Math. Comp. 46 1986 119 133
    • (1986) Math. Comp. , vol.46 , pp. 119-133
    • Zennaro, M.1
  • 39
    • 0040726924 scopus 로고
    • Natural Runge-Kutta and projection methods
    • M. Zennaro Natural Runge-Kutta and projection methods Numer. Math. 53 1988 423 438
    • (1988) Numer. Math. , vol.53 , pp. 423-438
    • Zennaro, M.1


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