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A P-stable singly diagonally implicit Runge-Kutta-Nyström method. (English) Zbl 0939.65097
A fifth-order singly diagonally Runge-Kutta-Nyström method is derived. The new method is constrained to being P-stable and is thus suitable for solving problems whose solution is dominated by oscillatory behaviour. The free parameters are chosen to achieve low values of some norms of the error constant vectors. The high order is shown to advantage in some constant stepsize experiments.

MSC:
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems, general theory
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
65L05 Numerical methods for initial value problems
65L20 Stability and convergence of numerical methods for ordinary differential equations
65L50 Mesh generation, refinement, and adaptive methods for ordinary differential equations
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