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Optimized Runge-Kutta pairs for problems with oscillating solutions. (English) Zbl 1013.65073
Summary: Three types of methods for integrating periodic initial value problems are presented. These methods are (i) phase-fitted, (ii) zero dissipation (iii) both zero dissipative and phase fitted. Some particular modifications of well-known explicit Runge-Kutta pairs of orders five and four are constructed. Numerical experiments show the efficiency of the new pairs in a wide range of oscillatory problems.

65L06Multistep, Runge-Kutta, and extrapolation methods
65L05Initial value problems for ODE (numerical methods)
34A34Nonlinear ODE and systems, general
65L50Mesh generation and refinement (ODE)
34C10Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory
34C25Periodic solutions of ODE
Full Text: DOI
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