E. Hairer and G. Wanner, Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems (Springer-Verlag, Berlin, 1996).
J. C. Butcher, Numerical Methods for Ordinary Differential Equations, 2nd ed. (Wiley, Chichester, 2008).
A. Kværnø, “Singly diagonally implicit Runge–Kutta methods with an explicit first stage,” BIT 44 (3), 489–502 (2004).
L. M. Skvortsov, “Diagonally implicit Runge–Kutta methods for stiff problems,” Comput. Math. Math. Phys. 46 (12), 2110–2123 (2006).
S. Gonzalez-Pinto, D. Hernandez-Abreu, and J. I. Montijano, “An efficient family of strongly A-stable Runge–Kutta collocation methods for stiff systems and DAEs. Part I: Stability and order results,” J. Comput. Appl. Math. 234 (4), 1105–1116 (2010).
G. Yu. Kulikov and S. K. Shindin, “On a family of cheap symmetric one-step methods of order four,” Computational Science—ICCS 2006, 6th International Conference, Reading, UK, May 28–31, 2006; Lect. Notes Comput. Sci. 3991, 781–785 (2006).
G. Yu. Kulikov and S. K. Shindin, “Adaptive nested implicit Runge–Kutta formulas of Gauss type,” Appl. Numer. Math. 59 (3–4), 707–722 (2009).
G. Yu. Kulikov, E. B. Kuznetsov, and E. Yu. Khrustaleva, “On global error control in nested implicit Runge–Kutta methods of the Gauss type,” Numer. Anal. Appl. 4 (3), 199–209 (2011).
G. Yu. Kulikov, “Embedded symmetric nested implicit Runge–Kutta methods of Gauss and Lobatto types for solving stiff ordinary differential equations and Hamiltonian systems,” Comput. Math. Math. Phys. 55 (6), 983–1003 (2015).
L. M. Skvortsov, “On implicit Runge–Kutta methods obtained as a result of the inversion of explicit methods,” Math. Models Comput. Simul. 9 (4), 498–510 (2017).
L. M. Skvortsov, “How to avoid accuracy and order reduction in Runge–Kutta Methods as applied to stiff problems,” Comput. Math. Math. Phys. 57 (7), 1124–1139 (2017).
L. M. Skvortsov, “Accuracy of Runge–Kutta methods applied to stiff problems,” Comput. Math. Math. Phys. 43 (9), 1320–1330 (2003).
E. Hairer, S. P. Nørsett, and G. Wanner, Solving Ordinary Differential Equations. I: Nonstiff Problems (Springer-Verlag, Berlin, 1987).
L. M. Skvortsov, “Model equations for accuracy investigation of Runge–Kutta methods,” Math. Models Comput. Simul. 2 (6), 800–811 (2010).
F. R. Gantmacher, The Theory of Matrices (Chelsea, New York, 1959; Nauka, Moscow, 1988).
L. M. Skvortsov, “Explicit multistep method for the numerical solution of stiff differential equations,” Comput. Math. Math. Phys. 47 (6), 915–923 (2007).
K. Dekker and J. G. Verwer, Stability of Runge–Kutta Methods for Stiff Nonlinear Differential Equations (North-Holland, Amsterdam, 1984).
M. V. Bulatov, A. V. Tygliyan, and S. S. Filippov, “A class of one-step one-stage methods for stiff systems of ordinary differential equations,” Comput. Math. Math. Phys. 51 (7), 1167–1180 (2011).
A. M. Zubanov and P. D. Shirkov, “Numerical study of one-step explicit-implicit methods of L-equivalent stiffly accurate two-stage Runge–Kutta schemes,” Math. Models Comput. Simul. 5 (4), 350–355 (2013).
J. C. Butcher and N. Rattenbury, “ARK methods for stiff problems,” Appl. Numer. Math. 53, 165–181 (2005).
L. Jay, “Convergence of a class of Runge–Kutta methods for differential-algebraic systems of index 2,” BIT 33 (1), 137–150 (1993).
L. Jay, “Convergence of Runge–Kutta methods for differential-algebraic systems of index 3,” Appl. Numer. Math. 17 (2), 97–118 (1995).