## Construction of explicit and generalized Runge-Kutta formulas of arbitrary order with rational parameters.(English)Zbl 0541.65047

The construction of explicit Runge-Kutta methods is considered with the requirement that all coefficients should be rational. It is shown how to generalize this construction for the differential equation $$y'=Ay+g(x,y)$$ in which the coefficients of the method are dependent on the matrix A. Stability questions for these so called ARK methods, where A is taken to be the Jacobian matrix, are investigated. In particular it is shown that all methods of this type are S-stable and conditions are derived under which they are also LS-stable.
Reviewer: J.C.Butcher

### MSC:

 65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations 65L20 Stability and convergence of numerical methods for ordinary differential equations

### Keywords:

explicit Runge-Kutta methods; ARK methods; S-stable; LS-stable
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### References:

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