Jackiewicz, Z.; Renaut, R.; Feldstein, A. Two-step Runge-Kutta methods. (English) Zbl 0732.65064 SIAM J. Numer. Anal. 28, No. 4, 1165-1182 (1991). The authors consider two-step Runge-Kutta methods for the problem \(y'(x)=f(y(x)), y(a)=y_ 0, f:R^ q\to R^ q;\) they are compared with one-step methods. Order conditions are derived using the theory of E. Hairer and G. Wanner [Computing 11, 287-303 (1973; Zbl 0271.65048)] and listed up to order 4. Stability properties of the methods with respect to the test equation \(y'=ay, a\in {\mathbb{C}}\) are presented and A-stable methods of order 2 are characterized. Reviewer: A.de Castro (Sevilla) Cited in 21 Documents MSC: 65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations 65L05 Numerical methods for initial value problems involving ordinary differential equations 65L20 Stability and convergence of numerical methods for ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems Keywords:two-step Runge-Kutta methods; Order conditions; Stability Citations:Zbl 0271.65048 PDFBibTeX XMLCite \textit{Z. Jackiewicz} et al., SIAM J. Numer. Anal. 28, No. 4, 1165--1182 (1991; Zbl 0732.65064) Full Text: DOI