×

zbMATH — the first resource for mathematics

Perturbed collocation and Runge-Kutta methods. (English) Zbl 0471.65045

MSC:
65L05 Numerical methods for initial value problems
65L20 Stability and convergence of numerical methods for ordinary differential equations
PDF BibTeX XML Cite
Full Text: DOI EuDML
References:
[1] Burrage, K.: High order algebraically stable Runge-Kutta methods BIT18, 373-383 (1978) · Zbl 0401.65049 · doi:10.1007/BF01932017
[2] Burrage, K.: A special family of Runge-Kutta methods for solving stiff differential equations. BIT18, 22-41 (1978) · Zbl 0384.65034 · doi:10.1007/BF01947741
[3] Butcher, J.C.: Integration processes based on Radau quadrature formulas. Math. Comput.18, 233-244 (1964) · Zbl 0123.11702 · doi:10.1090/S0025-5718-1964-0165693-1
[4] Butcher, J.C., Burrage, K.: Stability criteria for implicit Runge-Kutta methods. SIAM J. Numer. Anal.16, 46-57 (1979) · Zbl 0396.65043 · doi:10.1137/0716004
[5] Chipman, F.H.: A note on implicitA-stableR-K methods with parameters. BIT16, 223-227 (1976) · Zbl 0328.65039 · doi:10.1007/BF01931373
[6] Dieudonné, J.: Foundations of modern analysis. AP 1960, 1969 · Zbl 0100.04201
[7] Ehle, B.L.: On Padé approximations to the exponential function andA-stable methods for the numerical solution of initial value problems. Research Report CSRR2010, 1969, Waterloo, Canada, see also BIT8, 276-278 (1968) and SIAM J. Math. Anal.4, 671-680 (1973) · Zbl 0176.14604
[8] Nørsett, S.P.:C-polynomials for rational approximations to the exponential function. Numer. Math.25, 39-56 (1975) · Zbl 0299.65010 · doi:10.1007/BF01419527
[9] Nørsett, S.P., Wanner, G.: The real-pole sandwich for rational approximations and oscillation equations. BIT19, 79-94 (1979) · Zbl 0413.65011 · doi:10.1007/BF01931224
[10] Wanner, G.: A short proof on nonlinearA-stability. BIT16, 226-227 (1976) · Zbl 0329.65048 · doi:10.1007/BF01931374
[11] Wanner, G., Hairer, E., Nørsett, S.P.: Order stars and stability theorems. BIT18, 475-489 (1978) · Zbl 0444.65039 · doi:10.1007/BF01932026
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.