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Explicit two-step Runge-Kutta methods. (English) Zbl 0849.65055

This paper analyses the class of explicit two-step Runge-Kutta methods. It is shown that for methods of order 5 or less, these methods require the same number of function evaluations as a Runge-Kutta method of one order less. In particular, a 4-stage order 5 method is constructed and some numerical tests are performed.

MSC:

65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
65L05 Numerical methods for initial value problems involving ordinary differential equations

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References:

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