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Two-step Runge-Kutta methods. (English) Zbl 0732.65064

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.

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

Citations:

Zbl 0271.65048
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