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Zbl 0768.65041
Cong, Nguyen huu
$A$-stable diagonally implicit Runge-Kutta-Nyström methods for parallel computers. (English)
[J] Numer. Algorithms 4, No.3, 263-281 (1993). ISSN 1017-1398; ISSN 1572-9265/e

For the numerical solution of second order differential equations $y'' = f(y)$ 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 $y'' = \lambda y$, $\lambda < 0$) are investigated, and many numerical experiments are presented.
[E.Hairer (Genève)]

MSC 2000:: *65L06 Multistep, Runge-Kutta, and extrapolation methods
65Y05 Parallel computation (numerical methods)
65L20 Stability of numerical methods for ODE
34A34 Nonlinear ODE and systems, general

Keywords: predictor-corrector methods; $A$-stability; $A$-stable methods; second order differential equations; fully implicit Runge-Kutta Nyström methods; diagonally implicit iteration; parallel computation; order of convergence; numerical experiments

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