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A note on a diagonally implicit Runge-Kutta-Nyström method. (English) Zbl 0637.65065
For the numerical integration of the special second-order initial value problem y '' =f(t,y),y(t 0 )=y 0 ,y ' (t 0 )=y 0 ' it is often advantageous applying a direct method for this type of differential equations, rather than rewriting that to its first-order form. Fourth-order accurate diagonally implicit (or semi-explicit) Runge- Kutta-Nyström methods with only 2 stages are shown can be obtained. The scheme is given with the largest interval (0,12) of periodicity, and the requirement of P-stability decreases the order to 2.
Reviewer: L.M.Berkovich
MSC:
65L05Initial value problems for ODE (numerical methods)
65L20Stability and convergence of numerical methods for ODE
34A34Nonlinear ODE and systems, general