On the $BN$ stability of the Runge-Kutta methods
Abstract: In this note sufficient conditions that let Runge-Kutta s stages methods of at least order s be BN stable are given.
- Kevin Burrage and J. C. Butcher, Stability criteria for implicit Runge-Kutta methods, SIAM J. Numer. Anal. 16 (1979), no. 1, 46–57. MR 518683, DOI https://doi.org/10.1137/0716004
- Kevin Burrage, A special family of Runge-Kutta methods for solving stiff differential equations, BIT 18 (1978), no. 1, 22–41. MR 483458, DOI https://doi.org/10.1007/BF01947741
- J. C. Butcher, Implicit Runge-Kutta processes, Math. Comp. 18 (1964), 50–64. MR 159424, DOI https://doi.org/10.1090/S0025-5718-1964-0159424-9
- Kevin Burrage, High order algebraically stable Runge-Kutta methods, BIT 18 (1978), no. 4, 373–383. MR 520749, DOI https://doi.org/10.1007/BF01932017
- Michel Crouzeix, Sur la $B$-stabilité des méthodes de Runge-Kutta, Numer. Math. 32 (1979), no. 1, 75–82 (French, with English summary). MR 525638, DOI https://doi.org/10.1007/BF01397651
- Germund G. Dahlquist, A special stability problem for linear multistep methods, Nordisk Tidskr. Informationsbehandling (BIT) 3 (1963), 27–43. MR 170477, DOI https://doi.org/10.1007/bf01963532
K. Burrage & J. C. Butcher, "Stability criteria for implicit Runge-Kutta methods," SIAM J. Numer. Anal., v. 1, 1979, pp. 46-57.
K. Burrage, "A special family of Runge-Kutta methods for solving stiff differential equations," BIT, v. 18, 1978, pp. 24-71.
J. C. Butcher, "Implicit Runge-Kutta processes," Math. Comp., v. 18, 1964, pp. 50-64.
K. Burrage, "High order algebraically stable Runge-Kutta methods," BIT, v. 18, 1978, pp. 373-383.
M. Crouzeix, "Sur la BN-stabilité des méthodes de Runge-Kutta," Numer. Math., v. 82, 1979, pp. 32-75.
G. Dahlquist, "A special stability problem for linear multistep methods," BIT, v. 3, 1963, pp. 27-43.
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