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Frequency determination and step-length control for exponentially-fitted Runge-Kutta methods. (English) Zbl 0991.65062
Summary: An exponentially fitted Runge-Kutta (EFRK) fifth-order method with six stages is constructed, which exactly integrates first-order differential initial-value problems whose solutions are linear combinations of functions of the form {exp(ωx),exp(-ωx)}, (ω or i). By combining this EFRK method with an equivalent classical embedded (4,5) Runge-Kutta method, a technique is developed for the estimation of the occurring ω-values. Error and step-length control is carried out by using the Richardson extrapolation procedure. Some numerical experiments show the efficiency of the introduced methods.
MSC:
65L06Multistep, Runge-Kutta, and extrapolation methods
65L05Initial value problems for ODE (numerical methods)
34A34Nonlinear ODE and systems, general
65L50Mesh generation and refinement (ODE)
65L70Error bounds (numerical methods for ODE)