메뉴 건너뛰기




Volumn 33, Issue 3, 1996, Pages 917-936

A general family of explicit Runge-Kutta pairs of orders 6(5)

Author keywords

Initial value problems; Pairs of embedded methods; Runge Kutta

Indexed keywords


EID: 0001394474     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/0733046     Document Type: Article
Times cited : (35)

References (23)
  • 1
    • 84968483682 scopus 로고
    • On the attainable order of Runge-Kutta methods
    • J. C. BUTCHER, On the attainable order of Runge-Kutta methods, Math. Comp., 19 (1965), pp. 408-417.
    • (1965) Math. Comp. , vol.19 , pp. 408-417
    • Butcher, J.C.1
  • 3
    • 0008733712 scopus 로고
    • A new embedded pair of Runge-Kutta formulas of order 5 and 6
    • M. CALVO, J. I. MONTUANO, AND L. RANDEZ, A new embedded pair of Runge-Kutta formulas of order 5 and 6, Comput. Math. Appl., 20 (1990), pp. 15-24.
    • (1990) Comput. Math. Appl. , vol.20 , pp. 15-24
    • Calvo, M.1    Montuano, J.I.2    Randez, L.3
  • 4
    • 0014562199 scopus 로고
    • The complete solution of the fifth order Runge-Kutta equations
    • C. R. CASSITY, The complete solution of the fifth order Runge-Kutta equations, SIAM J. Numer. Anal., 6 (1969), pp. 432-436.
    • (1969) SIAM J. Numer. Anal. , vol.6 , pp. 432-436
    • Cassity, C.R.1
  • 5
    • 0039179839 scopus 로고
    • High order explicit Runge-Kutta formulae, their uses and their limitations
    • A. R. CURTIS, High order explicit Runge-Kutta formulae, their uses and their limitations, J. Inst. Math. Appl., 16 (1975), pp. 35-55.
    • (1975) J. Inst. Math. Appl. , vol.16 , pp. 35-55
    • Curtis, A.R.1
  • 7
    • 0018991720 scopus 로고
    • A family of embedded Runge-Kutta formulae
    • J. R. DORMAND AND P. J. PRINCE, A family of embedded Runge-Kutta formulae, J. Comput. Appl. Math., 6 (1980), pp. 19-26.
    • (1980) J. Comput. Appl. Math. , vol.6 , pp. 19-26
    • Dormand, J.R.1    Prince, P.J.2
  • 8
    • 0022734765 scopus 로고
    • A reconsideration of some embedded Runge-Kutta formulae
    • _, A reconsideration of some embedded Runge-Kutta formulae, J. Comput. Appl. Math., 15 (1986), pp. 203-211.
    • (1986) J. Comput. Appl. Math. , vol.15 , pp. 203-211
  • 9
    • 0023312263 scopus 로고
    • Two FORTRAN packages for assessing initial value methods
    • W. H. ENRIGHT AND J. D. PRYCE, Two FORTRAN packages for assessing initial value methods, ACM Trans. Math. Software, 13 (1987), pp. 1-27.
    • (1987) ACM Trans. Math. Software , vol.13 , pp. 1-27
    • Enright, W.H.1    Pryce, J.D.2
  • 12
    • 0004864925 scopus 로고
    • A Runge-Kutta method of order 10
    • E. HAIRER, A Runge-Kutta method of order 10, J. Inst. Math. Appl., 21 (1978), pp. 47-59.
    • (1978) J. Inst. Math. Appl. , vol.21 , pp. 47-59
    • Hairer, E.1
  • 13
    • 0001897217 scopus 로고
    • A one-step method of order 10 for y″ = f (x, y)
    • E. HAIRER, A one-step method of order 10 for y″ = f (x, y), IMA J. Numer. Anal., 2 (1982), pp. 83-94.
    • (1982) IMA J. Numer. Anal. , vol.2 , pp. 83-94
    • Hairer, E.1
  • 14
  • 16
    • 0001312539 scopus 로고
    • Runge-Kutta pairs for periodic initial value problems
    • G. PAPAGEORGIOU, C. TSITOURAS, AND S. N. PAPAKOSTAS, Runge-Kutta pairs for periodic initial value problems, Computing, 51 (1993), pp. 151-163.
    • (1993) Computing , vol.51 , pp. 151-163
    • Papageorgiou, G.1    Tsitouras, C.2    Papakostas, S.N.3
  • 17
    • 49149135749 scopus 로고
    • High order embedded Runge-Kutta formulae
    • P. J. PRINCE AND J. R. DORMAND, High order embedded Runge-Kutta formulae, J. Comput. Appl. Math., 7 (1981), pp. 67-75.
    • (1981) J. Comput. Appl. Math. , vol.7 , pp. 67-75
    • Prince, P.J.1    Dormand, J.R.2
  • 18
    • 0026216091 scopus 로고
    • Numerical comparisons of some explicit Runge-Kutta pairs of orders 4 through 8
    • P. SHARP, Numerical comparisons of some explicit Runge-Kutta pairs of orders 4 through 8, ACM Trans. Math. Software, 17 (1991).
    • (1991) ACM Trans. Math. Software , vol.17
    • Sharp, P.1
  • 19
    • 0038440068 scopus 로고
    • Explicit Runge-Kutta pairs with one more derivative evaluation than minimum
    • P. W. SHARP AND E. SMART, Explicit Runge-Kutta pairs with one more derivative evaluation than minimum, SIAM J. Sci. Statist. Comput., 14 (1993), pp. 338-348.
    • (1993) SIAM J. Sci. Statist. Comput. , vol.14 , pp. 338-348
    • Sharp, P.W.1    Smart, E.2
  • 20
    • 0000468784 scopus 로고
    • Explicit Runge-Kutta methods with estimates of the local truncation error
    • J. H. VERNER, Explicit Runge-Kutta methods with estimates of the local truncation error, SIAM J. Numer. Anal., 15 (1978), pp. 772-790.
    • (1978) SIAM J. Numer. Anal. , vol.15 , pp. 772-790
    • Verner, J.H.1
  • 21
    • 0025507498 scopus 로고
    • A contrast of some Runge-Kutta formula pairs
    • _, A contrast of some Runge-Kutta formula pairs, SIAM J. Numer. Anal., 27 (1990), pp. 1332-1344.
    • (1990) SIAM J. Numer. Anal. , vol.27 , pp. 1332-1344
  • 22
    • 0026142627 scopus 로고
    • Some Runge-Kutta formula pairs
    • _, Some Runge-Kutta formula pairs, SIAM J. Numer. Anal., 28 (1991), pp. 496-511.
    • (1991) SIAM J. Numer. Anal. , vol.28 , pp. 496-511
  • 23
    • 0342616178 scopus 로고
    • Strategies for deriving new explicit Runge-Kutta pairs
    • _, Strategies for deriving new explicit Runge-Kutta pairs, Annals of Numerical Mathematics, 1 (1994), pp. 225-244.
    • (1994) Annals of Numerical Mathematics , vol.1 , pp. 225-244


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.