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$A$-stable diagonally implicit Runge-Kutta-Nyström methods for parallel computers. (English) Zbl 0768.65041
For the numerical solution of second order differential equations ${y}^{\text{'}\text{'}}=f\left(y\right)$ the author considers fully implicit Runge-Kutta Nyström methods and applies diagonally implicit iteration for the solution of the nonlinear system. This makes the methods suitable for parallel computation. The order of convergence and the stability of the methods (for the scalar test equation ${y}^{\text{'}\text{'}}=\lambda y$, $\lambda <0$) are investigated, and many numerical experiments are presented.
##### MSC:
 65L06 Multistep, Runge-Kutta, and extrapolation methods 65Y05 Parallel computation (numerical methods) 65L20 Stability and convergence of numerical methods for ODE 34A34 Nonlinear ODE and systems, general
RODAS
##### References:
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