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Zbl 0974.65076
Franco, J.M.; Gómez, I.; Rández, L.
Four-stage symplectic and P-stable SDIRKN methods with dispersion of high order. (English)
[J] Numer. Algorithms 26, No.4, 347-363 (2001). ISSN 1017-1398; ISSN 1572-9265/e

For a second order stiff initial value problem having periodic solutions, the authors investigate the construction of four-stage fourth-order symplectic and P-stable singly diagonally implicit Runge-Kutta-Nyström (SDIRKN) methods which have high order of dispersion (order 8). Conditions of symplecticness, order conditions for order 4, conditions of symmetry and conditions of stability are imposed and are solved to obtain such methods. Numerical experiments are considered for four test problems and numerical results show that SDIRKN methods perform very efficiently.
[Iulian Coroian (Baia Mare)]

MSC 2000:: *65L06 Multistep, Runge-Kutta, and extrapolation methods
65L05 Initial value problems for ODE (numerical methods)
65L20 Stability of numerical methods for ODE
34A34 Nonlinear ODE and systems, general

Keywords: singly diagonally implicit Runge-Kutta-Nyström methods; periodic stiff problems; P-stability; symplectic methods; dispersion; numerical experiments; test problems

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