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Volumn 459, Issue 2032, 2003, Pages 797-815

Efficient numerical methods for the solution of stiff initial-value problems and differential algebraic equations

Author keywords

A stability; Differential algebraic equations; Stiff initial value problems

Indexed keywords

COMPUTER PROGRAM; MATHEMATICAL ANALYSIS; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; MATHEMATICS; PROBLEM SOLVING; REVIEW;

EID: 1542722129     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2003.1130     Document Type: Review
Times cited : (68)

References (33)
  • 1
    • 0001266425 scopus 로고
    • Diagonally implicit Runge-Kutta methods for stiff ODEs
    • Alexander, R. 1977 Diagonally implicit Runge-Kutta methods for stiff ODEs. SIAM J. Numer. Analysis 14, 1006-1021.
    • (1977) SIAM J. Numer. Analysis , vol.14 , pp. 1006-1021
    • Alexander, R.1
  • 2
    • 0012189284 scopus 로고
    • An efficient solution process for implicit Runge-Kutta methods
    • Bickart, T. A. 1977 An efficient solution process for implicit Runge-Kutta methods. SIAM J. Numer. Analysis 14, 1022-1027.
    • (1977) SIAM J. Numer. Analysis , vol.14 , pp. 1022-1027
    • Bickart, T.A.1
  • 5
    • 0002612111 scopus 로고
    • A special family of Runge-Kutta methods for solving stiff differential equations
    • Burrage, K. 1978 A special family of Runge-Kutta methods for solving stiff differential equations. BIT 18, 22-41.
    • (1978) BIT , vol.18 , pp. 22-41
    • Burrage, K.1
  • 6
    • 0346498498 scopus 로고
    • Efficiently implementable algebraically stable Runge-Kutta methods
    • Burrage, K. 1982 Efficiently implementable algebraically stable Runge-Kutta methods. SIAM J. Numer. Analysis 19, 245-258.
    • (1982) SIAM J. Numer. Analysis , vol.19 , pp. 245-258
    • Burrage, K.1
  • 7
    • 0000366955 scopus 로고
    • An implementation of singly implicit Runge-Kutta methods
    • Burrage, K., Butcher, J. C. & Chipman, F. H. 1980 An implementation of singly implicit Runge-Kutta methods. BIT 20, 326-340.
    • (1980) BIT , vol.20 , pp. 326-340
    • Burrage, K.1    Butcher, J.C.2    Chipman, F.H.3
  • 8
    • 84968496738 scopus 로고
    • Implicit Runge-Kutta processes
    • Butcher, J. C. 1964 Implicit Runge-Kutta processes. Math. Comp. 18, 50-64.
    • (1964) Math. Comp. , vol.18 , pp. 50-64
    • Butcher, J.C.1
  • 9
    • 0000194464 scopus 로고
    • On the implementation of implicit Runge-Kutta methods
    • Butcher, J. C. 1976 On the implementation of implicit Runge-Kutta methods. BIT 6, 237-240.
    • (1976) BIT , vol.6 , pp. 237-240
    • Butcher, J.C.1
  • 10
    • 1542666003 scopus 로고
    • Linear and nonlinear stability for general linear methods
    • Butcher, J. C. 1987 Linear and nonlinear stability for general linear methods. BIT 27, 182-189.
    • (1987) BIT , vol.27 , pp. 182-189
    • Butcher, J.C.1
  • 11
    • 0025448875 scopus 로고
    • Towards efficient Runge-Kutta methods for stiff systems
    • Butcher, J. C. & Cash, J. R. 1990 Towards efficient Runge-Kutta methods for stiff systems. SIAM J. Numer. Analysis 27, 753-761.
    • (1990) SIAM J. Numer. Analysis , vol.27 , pp. 753-761
    • Butcher, J.C.1    Cash, J.R.2
  • 13
    • 0034509044 scopus 로고    scopus 로고
    • Modified extended backward differentiation formulae for the numerical solution of stiff initial-value problems in ODEs and DAEs
    • Cash, J. R. 2000 Modified extended backward differentiation formulae for the numerical solution of stiff initial-value problems in ODEs and DAEs. J. Comput. Appl. Math. 125, 117-130.
    • (2000) J. Comput. Appl. Math. , vol.125 , pp. 117-130
    • Cash, J.R.1
  • 15
    • 11044230975 scopus 로고
    • A special stability problem for linear multistep methods
    • Dahlquist, G. 1963 A special stability problem for linear multistep methods. BIT 3, 27-43.
    • (1963) BIT , vol.3 , pp. 27-43
    • Dahlquist, G.1
  • 16
    • 0016443950 scopus 로고
    • Comparing numerical methods for stiff systems of ODEs
    • Enright, W. H., Hull, T. E. & Lindberg, B. 1975 Comparing numerical methods for stiff systems of ODEs. BIT 15, 10-48.
    • (1975) BIT , vol.15 , pp. 10-48
    • Enright, W.H.1    Hull, T.E.2    Lindberg, B.3
  • 19
    • 84968503426 scopus 로고
    • A note on trapezoidal methods for the solution of initial value problems
    • Gourlay, A. R. 1970 A note on trapezoidal methods for the solution of initial value problems. Math. Comp. 24, 629-633.
    • (1970) Math. Comp. , vol.24 , pp. 629-633
    • Gourlay, A.R.1
  • 21
    • 0038394260 scopus 로고
    • Algebraically stable and implementable Runge-Kutta methods of high order
    • Hairer, E. &Wanner, G. 1981 Algebraically stable and implementable Runge-Kutta methods of high order. SIAM J. Numer. Analysis 18, 1098-1108.
    • (1981) SIAM J. Numer. Analysis , vol.18 , pp. 1098-1108
    • Hairer, E.1    Wanner, G.2
  • 24
    • 0003321806 scopus 로고
    • The numerical solution of differential algebraic systems by Runge-Kutta methods
    • Springer
    • Hairer, E., Lubich, Ch. & Roche, M. 1989 The numerical solution of differential algebraic systems by Runge-Kutta methods. Lecture Notes in Mathematics, vol. 1409. Springer.
    • (1989) Lecture Notes in Mathematics , pp. 1409
    • Hairer, E.1    Lubich, Ch.2    Roche, M.3
  • 25
    • 0002445594 scopus 로고
    • LSODE and LSODI, two new initial-value ordinary differential equation solvers
    • Hindmarsh, A. C. 1980 LSODE and LSODI, two new initial-value ordinary differential equation solvers. ACM-Signum Newsletter, vol. 15, pp. 10-11.
    • (1980) ACM-Signum Newsletter , vol.15 , pp. 10-11
    • Hindmarsh, A.C.1
  • 26
    • 0002117326 scopus 로고
    • Efficient integration methods for stiff systems of ordinary differential equations
    • Liniger, W. & Willoughby, R. A. 1970 Efficient integration methods for stiff systems of ordinary differential equations. SIAM J. Numer. Analysis 7, 47-66.
    • (1970) SIAM J. Numer. Analysis , vol.7 , pp. 47-66
    • Liniger, W.1    Willoughby, R.A.2
  • 27
    • 0003433657 scopus 로고    scopus 로고
    • Test set for initial value problem solvers
    • Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands
    • Lioen, W. M. & de Swart, J. 1998 Test set for initial value problem solvers. CWI Internal Report MAS-R9832. Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands.
    • (1998) CWI Internal Report MAS-R9832
    • Lioen, W.M.1    De Swart, J.2
  • 28
    • 0005737807 scopus 로고
    • Runge-Kutta methods with a multiple real eigenvalue only
    • Nørsett, S. P. 1976 Runge-Kutta methods with a multiple real eigenvalue only. BIT 16, 388-393.
    • (1976) BIT , vol.16 , pp. 388-393
    • Nørsett, S.P.1
  • 29
    • 0022767918 scopus 로고
    • Order results for implicit Runge-Kutta methods applied to differential algebraic equations
    • Petzold, L. R. 1986 Order results for implicit Runge-Kutta methods applied to differential algebraic equations. SIAM J. Numer. Analysis 23, 837-857.
    • (1986) SIAM J. Numer. Analysis , vol.23 , pp. 837-857
    • Petzold, L.R.1
  • 30
    • 84968497765 scopus 로고
    • On the stability and accuracy of one-step methods for solving stiff systems of ordinary differential equations
    • Prothero, A. & Robinson, A. 1974 On the stability and accuracy of one-step methods for solving stiff systems of ordinary differential equations. Math. Comp. 28, 145-162.
    • (1974) Math. Comp. , vol.28 , pp. 145-162
    • Prothero, A.1    Robinson, A.2
  • 31
    • 84966208410 scopus 로고
    • Differential algebraic systems as differential equations on manifolds
    • Rheinboldt, W. C. 1984 Differential algebraic systems as differential equations on manifolds. Math. Comp. 43, 473-482.
    • (1984) Math. Comp. , vol.43 , pp. 473-482
    • Rheinboldt, W.C.1
  • 32
    • 84968470192 scopus 로고
    • On the efficient implementation of implicit Runge-Kutta methods
    • Varah, J. M. 1979 On the efficient implementation of implicit Runge-Kutta methods. Math. Comp. 33, 557-561.
    • (1979) Math. Comp. , vol.33 , pp. 557-561
    • Varah, J.M.1
  • 33
    • 0009419915 scopus 로고
    • A note on unconditionally stable linear multistep methods
    • Widlund, O. B. 1963 A note on unconditionally stable linear multistep methods. BIT 7, 65-70.
    • (1963) BIT , vol.7 , pp. 65-70
    • Widlund, O.B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.