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Volumn 22, Issue 1-3 SPEC. ISS., 1996, Pages 263-277

Runge-Kutta research in Trondheim

Author keywords

[No Author keywords available]

Indexed keywords

DIFFERENTIAL EQUATIONS;

EID: 0030287581     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0168-9274(96)00037-2     Document Type: Article
Times cited : (18)

References (68)
  • 1
    • 0001266425 scopus 로고
    • Diagonally implicit Runge-Kutta methods for stiff O.D.Es
    • R.K. Alexander, Diagonally implicit Runge-Kutta methods for stiff O.D.Es, SIAM J. Numer. Anal. 14 (1977) 1006-1024.
    • (1977) SIAM J. Numer. Anal. , vol.14 , pp. 1006-1024
    • Alexander, R.K.1
  • 2
    • 0347043199 scopus 로고
    • Runge-Kutta methods and differential-algebraic systems
    • Iowa State University, Ames
    • R.K. Alexander and J.J. Coyle, Runge-Kutta methods and differential-algebraic systems, Technical Report, Iowa State University, Ames (1988).
    • (1988) Technical Report
    • Alexander, R.K.1    Coyle, J.J.2
  • 4
    • 0001197485 scopus 로고
    • A class of A-stable methods
    • O. Axelson, A class of A-stable methods, BIT 9 (1969) 185-199.
    • (1969) BIT , vol.9 , pp. 185-199
    • Axelson, O.1
  • 5
    • 85162725910 scopus 로고
    • Disrectization errors for well-set Cauchy problems
    • G. Birkhoff and R.S. Varga, Disrectization errors for well-set Cauchy problems, Internat. J. Math. Phys. 44 (1965) 1-23.
    • (1965) Internat. J. Math. Phys. , vol.44 , pp. 1-23
    • Birkhoff, G.1    Varga, R.S.2
  • 6
    • 0346412901 scopus 로고
    • Shape preserving interpolation for plotting solutions of ODEs
    • R.W. Brankin and I. Gladwell, Shape preserving interpolation for plotting solutions of ODEs, IMA J. Numer. Anal. 9 (1989) 555-566.
    • (1989) IMA J. Numer. Anal. , vol.9 , pp. 555-566
    • Brankin, R.W.1    Gladwell, I.2
  • 7
    • 0002351173 scopus 로고
    • Stability criteria for implicit Runge-Kutta methods
    • K. Burrage and J.C. Butcher, Stability criteria for implicit Runge-Kutta methods, SIAM J. Numer. Anal. 16 (1979) 46-57.
    • (1979) SIAM J. Numer. Anal. , vol.16 , pp. 46-57
    • Burrage, K.1    Butcher, J.C.2
  • 8
    • 0000366955 scopus 로고
    • An implementation of singly-implicit Runge-Kutta methods
    • K. Burrage, J.C. Butcher and F.H. Chipman, An implementation of singly-implicit Runge-Kutta methods, BIT 27 (1980) 326-340.
    • (1980) BIT , vol.27 , pp. 326-340
    • Burrage, K.1    Butcher, J.C.2    Chipman, F.H.3
  • 9
    • 0016647175 scopus 로고
    • A stability property of implicit Runge-Kutta methods
    • J.C. Butcher, A stability property of implicit Runge-Kutta methods, BIT 15 (1975) 358-361.
    • (1975) BIT , vol.15 , pp. 358-361
    • Butcher, J.C.1
  • 10
    • 84968496738 scopus 로고
    • Implicit Runge-Kutta processes
    • J.C. Butcher, Implicit Runge-Kutta processes, Math. Comp. 18 (1964) 50-64.
    • (1964) Math. Comp. , vol.18 , pp. 50-64
    • Butcher, J.C.1
  • 12
    • 0345781827 scopus 로고
    • A lower bound for the number of stages of an explicit continuous Runge-Kutta method to obtain convergence of given order
    • J.M. Carnicer, A lower bound for the number of stages of an explicit continuous Runge-Kutta method to obtain convergence of given order, BIT 31 (1991) 364-368.
    • (1991) BIT , vol.31 , pp. 364-368
    • Carnicer, J.M.1
  • 13
    • 0001354138 scopus 로고
    • Diagonally implicit Runge-Kutta formulae with error estimates
    • J.R. Cash, Diagonally implicit Runge-Kutta formulae with error estimates, J. Inst. Math. Appl. 24 (1979) 293-301.
    • (1979) J. Inst. Math. Appl. , vol.24 , pp. 293-301
    • Cash, J.R.1
  • 15
    • 0002089844 scopus 로고
    • Sur la B-stabilité des méthodes de Runge-Kutta
    • M. Crouzeix, Sur la B-stabilité des méthodes de Runge-Kutta, Numer. Math. 32 (1979) 75-82.
    • (1979) Numer. Math. , vol.32 , pp. 75-82
    • Crouzeix, M.1
  • 16
    • 11044230975 scopus 로고
    • A special stability problem for linear multistep methods
    • G. Dahlquist, A special stability problem for linear multistep methods, BIT 3 (1963) 27-43.
    • (1963) BIT , vol.3 , pp. 27-43
    • Dahlquist, G.1
  • 18
    • 0005152490 scopus 로고
    • High order A-stable methods for the numerical solution of systems of D.E.'s
    • B.L. Ehle, High order A-stable methods for the numerical solution of systems of D.E.'s, BIT 8 (1968) 276-278.
    • (1968) BIT , vol.8 , pp. 276-278
    • Ehle, B.L.1
  • 19
    • 0001743435 scopus 로고
    • A new error-control for initial value solvers
    • W.H. Enright, A new error-control for initial value solvers, Appl. Math. Comput. 31 (1989) 288-301.
    • (1989) Appl. Math. Comput. , vol.31 , pp. 288-301
    • Enright, W.H.1
  • 20
    • 0010965403 scopus 로고
    • Analysis of error control strategies for continuous Runge-Kutta methods
    • W.H. Enright, Analysis of error control strategies for continuous Runge-Kutta methods, SIAM J. Numer. Anal. 26 (1989) 588-599.
    • (1989) SIAM J. Numer. Anal. , vol.26 , pp. 588-599
    • Enright, W.H.1
  • 25
    • 0004716975 scopus 로고
    • Highest possible order of algebraically stable diagonally implicit Runge-Kutta methods
    • E. Hairer, Highest possible order of algebraically stable diagonally implicit Runge-Kutta methods, BIT 20 (1980) 254-256.
    • (1980) BIT , vol.20 , pp. 254-256
    • Hairer, E.1
  • 26
    • 0001599522 scopus 로고
    • Error of Runge-Kutta methods for stiff problems studied via differential algebraic equations
    • E. Hairer, Ch. Lubich and M. Roche, Error of Runge-Kutta methods for stiff problems studied via differential algebraic equations, BIT 28 (1988) 678-700.
    • (1988) BIT , vol.28 , pp. 678-700
    • Hairer, E.1    Lubich, Ch.2    Roche, M.3
  • 28
    • 0026212379 scopus 로고
    • Highly continuous Runge-Kutta interpolants
    • D.J. Higham, Highly continuous Runge-Kutta interpolants, ACM Trans. Math. Software 17 (1991) 368-386.
    • (1991) ACM Trans. Math. Software , vol.17 , pp. 368-386
    • Higham, D.J.1
  • 29
    • 0039638076 scopus 로고
    • Fourth- and fifth-order, scaled Runge-Kutta algorithms for treating dense output
    • M.K. Horn, Fourth- and fifth-order, scaled Runge-Kutta algorithms for treating dense output, SIAM J. Numer. Anal. 20 (1983) 558-568.
    • (1983) SIAM J. Numer. Anal. , vol.20 , pp. 558-568
    • Horn, M.K.1
  • 30
    • 0012111062 scopus 로고
    • Displacement or residual test in the application of implicit methods for stiff problems
    • N. Houbak, S.P. Nørsett and P.G. Thomsen, Displacement or residual test in the application of implicit methods for stiff problems, IMA J. Numer. Anal. 5 (1985) 297-305.
    • (1985) IMA J. Numer. Anal. , vol.5 , pp. 297-305
    • Houbak, N.1    Nørsett, S.P.2    Thomsen, P.G.3
  • 31
    • 0003545319 scopus 로고
    • On the theory of parallel Runge-Kutta methods
    • A. Iserles and S.P. Nørsett, On the theory of parallel Runge-Kutta methods, IMA J. Numer. Anal. 19 (1990) 463-488.
    • (1990) IMA J. Numer. Anal. , vol.19 , pp. 463-488
    • Iserles, A.1    Nørsett, S.P.2
  • 33
    • 0347742471 scopus 로고    scopus 로고
    • An analysis of the order of Runge-Kutta methods that use an iterative scheme to compute their internal stage values
    • to appear
    • K.R. Jackson, A. Kværnø and S.P. Nørsett, An analysis of the order of Runge-Kutta methods that use an iterative scheme to compute their internal stage values, BIT. to appear.
    • BIT
    • Jackson, K.R.1    Kværnø, A.2    Nørsett, S.P.3
  • 34
    • 0001968970 scopus 로고
    • The potential for parallelism in Runge-Kutta methods. Part 1: RK formulas in standard form
    • K.R. Jackson and S.P. Nørsett, The potential for parallelism in Runge-Kutta methods. Part 1: RK formulas in standard form, SIAM J. Numer. Anal. 32 (1995) 49-82.
    • (1995) SIAM J. Numer. Anal. , vol.32 , pp. 49-82
    • Jackson, K.R.1    Nørsett, S.P.2
  • 36
    • 0041617756 scopus 로고
    • On implicit Runge-Kutta methods with a stability function having distinct real poles
    • S.L. Keeling, On implicit Runge-Kutta methods with a stability function having distinct real poles, BIT 29 (1989) 91-109.
    • (1989) BIT , vol.29 , pp. 91-109
    • Keeling, S.L.1
  • 40
    • 0039357237 scopus 로고
    • Some aspects of parallel Runge-Kutta methods
    • University of Trondheim, Norway
    • I. Lie, Some aspects of parallel Runge-Kutta methods, Technical Report 3/87, University of Trondheim, Norway (1987).
    • (1987) Technical Report 3/87
    • Lie, I.1
  • 41
    • 0007013992 scopus 로고
    • C-polynomials for rational approximation to the exponential function
    • S.P. Nørsett, C-polynomials for rational approximation to the exponential function, Numer. Math. 25 (1975) 39-56.
    • (1975) Numer. Math. , vol.25 , pp. 39-56
    • Nørsett, S.P.1
  • 43
    • 0039949619 scopus 로고
    • Aspects of parallel Runge-Kutta methods
    • Numerical Methods for Ordinary Differential Equations, Springer, New York
    • S.P. Nørsett and H.H. Simonsen, Aspects of parallel Runge-Kutta methods, in: Numerical Methods for Ordinary Differential Equations, Lecture Notes in Mathematics 1386 (Springer, New York, 1987) 103-118.
    • (1987) Lecture Notes in Mathematics , vol.1386 , pp. 103-118
    • Nørsett, S.P.1    Simonsen, H.H.2
  • 44
    • 0021544958 scopus 로고
    • Embedded SDIRK-methods of basic order three
    • S.P. Nørsett and P.G. Thomsen, Embedded SDIRK-methods of basic order three, BIT 24 (1984) 634-646.
    • (1984) BIT , vol.24 , pp. 634-646
    • Nørsett, S.P.1    Thomsen, P.G.2
  • 45
    • 0022563559 scopus 로고
    • Local error control in SDIRK-methods
    • S.P. Nørsett and P.G. Thomsen, Local error control in SDIRK-methods, BIT 26 (1986) 100-113.
    • (1986) BIT , vol.26 , pp. 100-113
    • Nørsett, S.P.1    Thomsen, P.G.2
  • 46
    • 0022865958 scopus 로고
    • Switching between modified and fix-point iteration for implicit ODE-solvers
    • S.P. Nørsett and P.G. Thomsen, Switching between modified and fix-point iteration for implicit ODE-solvers, BIT 26 (1986) 339-348.
    • (1986) BIT , vol.26 , pp. 339-348
    • Nørsett, S.P.1    Thomsen, P.G.2
  • 47
    • 0007058183 scopus 로고
    • Perturbed collocation and Runge-Kutta methods
    • S.P. Nørsett and G. Wanner, Perturbed collocation and Runge-Kutta methods, Numer. Math. 36 (1981) 193-208.
    • (1981) Numer. Math. , vol.36 , pp. 193-208
    • Nørsett, S.P.1    Wanner, G.2
  • 49
    • 0345781824 scopus 로고
    • Real pole approximations to the exponential function
    • B. Orel, Real pole approximations to the exponential function, BIT 31 (1991) 144-159.
    • (1991) BIT , vol.31 , pp. 144-159
    • Orel, B.1
  • 52
    • 0029289420 scopus 로고
    • Alternative integration methods for problems in structural dynamics
    • B. Owren and H.H. Simonsen, Alternative integration methods for problems in structural dynamics, Comput. Methods Appl. Mech. Engrg. 122 (1995) 1-10.
    • (1995) Comput. Methods Appl. Mech. Engrg. , vol.122 , pp. 1-10
    • Owren, B.1    Simonsen, H.H.2
  • 53
    • 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
  • 54
    • 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
  • 55
    • 0022767918 scopus 로고
    • Order results for implicit Runge-Kutta methods applied to differential/algebraic systems
    • L.R. Petzold, Order results for implicit Runge-Kutta methods applied to differential/algebraic systems, SIAM J. Numer. Anal. 23 (1986) 837-852.
    • (1986) SIAM J. Numer. Anal. , vol.23 , pp. 837-852
    • Petzold, L.R.1
  • 56
    • 84968497765 scopus 로고
    • On the stability and accuracy of one-step methods for solving stiff systems of ordinary differential equations
    • A. Prothero and A. Robinson, On the stability and accuracy of one-step methods for solving stiff systems of ordinary differential equations, Math. Comp. 28 (1974) 145-162.
    • (1974) Math. Comp. , vol.28 , pp. 145-162
    • Prothero, A.1    Robinson, A.2
  • 57
    • 0342464269 scopus 로고
    • Implicit Runge-Kutta methods for differential algebraic equations
    • M. Roche, Implicit Runge-Kutta methods for differential algebraic equations, SIAM J. Numer. Anal. 26 (1989) 963-975.
    • (1989) SIAM J. Numer. Anal. , vol.26 , pp. 963-975
    • Roche, M.1
  • 59
    • 84966237458 scopus 로고
    • Some practical Runge-Kutta formulas
    • L. Shampine, Some practical Runge-Kutta formulas, SIAM J. Numer. Anal. 46 (1985) 135-150.
    • (1985) SIAM J. Numer. Anal. , vol.46 , pp. 135-150
    • Shampine, L.1
  • 60
    • 0022144651 scopus 로고
    • Interpolation for Runge-Kutta methods
    • L.F. Shampine, Interpolation for Runge-Kutta methods, SIAM J. Numer. Anal. 22 (1985) 1014-1027.
    • (1985) SIAM J. Numer. Anal. , vol.22 , pp. 1014-1027
    • Shampine, L.F.1
  • 62
    • 85163206922 scopus 로고
    • On higher order stable implicit methods for solving parabolic differential equations
    • R.S. Varga, On higher order stable implicit methods for solving parabolic differential equations, J. Math. Phys. 40 (1961) 220-231.
    • (1961) J. Math. Phys. , vol.40 , pp. 220-231
    • Varga, R.S.1
  • 63
    • 0027683528 scopus 로고
    • Differentiable interpolants for high-order Runge-Kutta methods
    • J. Verner, Differentiable interpolants for high-order Runge-Kutta methods, SIAM J. Numer. Anal. 30 (1993) 1446-1466.
    • (1993) SIAM J. Numer. Anal. , vol.30 , pp. 1446-1466
    • Verner, J.1
  • 64
    • 31644432026 scopus 로고
    • Order stars and stability theorems
    • G. Wanner, E. Hairer and S.P. Nørsett, Order stars and stability theorems, BIT 18 (1978) 475-489.
    • (1978) BIT , vol.18 , pp. 475-489
    • Wanner, G.1    Hairer, E.2    Nørsett, S.P.3
  • 65
    • 0001716997 scopus 로고
    • Some relationships between implicit Runge-Kutta, collocation and Lanczos τ methods, and their stability properties
    • K. Wright, Some relationships between implicit Runge-Kutta, collocation and Lanczos τ methods, and their stability properties, BIT 10 (1970) 217-227.
    • (1970) BIT , vol.10 , pp. 217-227
    • Wright, K.1
  • 66
    • 0022412915 scopus 로고
    • One-step collocation: Uniform superconvergence, predictor-corrector method, local error estimate
    • M. Zennaro, One-step collocation: uniform superconvergence, predictor-corrector method, local error estimate, SIAM J. Numer. Anal. 22 (1985) 1135-1152.
    • (1985) SIAM J. Numer. Anal. , vol.22 , pp. 1135-1152
    • Zennaro, M.1
  • 67
    • 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
  • 68
    • 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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