Butcher, John C.; Rattenbury, Nicolette ARK methods for stiff problems. (English) Zbl 1070.65059 Appl. Numer. Math. 53, No. 2-4, 165-181 (2005). The authors show that it is possible to generalize the almost Runge-Kutta (ARK)methods to stiff problems by adding a constant diagonal to the coefficient matrix \(A\). Reviewer: Emil Minchev (Tokyo) Cited in 14 Documents MSC: 65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations 65L05 Numerical methods for initial value problems involving ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems Keywords:almost Runge-Kutta methods; Stiff problems; A-stability PDF BibTeX XML Cite \textit{J. C. Butcher} and \textit{N. Rattenbury}, Appl. Numer. Math. 53, No. 2--4, 165--181 (2005; Zbl 1070.65059) Full Text: DOI OpenURL References: [1] Butcher, J.C., An introduction to “almost runge – kutta” methods, Appl. numer. math., 24, 331-342, (1997) · Zbl 0905.65085 [2] Butcher, J.C., ARK methods up to order five, Numer. algorithms, 17, 193-221, (1998) · Zbl 0907.65069 [3] Butcher, J.C., Numerical methods for ordinary differential equations, (2003), Wiley Chichester · Zbl 1032.65512 [4] Butcher, J.C.; Moir, N., Experiments with a new fifth order method, Numer. algorithms, 33, 137-151, (2003) · Zbl 1030.65081 [5] W. Wright, General Linear Methods with Inherent Runge-Kutta Stability, Ph.D. Thesis, Department of Mathematics, The University of Auckland, 2002 · Zbl 1016.65049 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.