Abstract
Explicit Runge-Kutta methods of order \(p\) with \(m\) stages, \(m= 1, 2, 3, 4\), are considered. It is assumed that \(p = m\) and that Richardson Extrapolation is additionally used. It is proved that not only are the combinations of the Richardson Extrapolation with the selected explicit Runge-Kutta methods more accurate than the underlying numerical methods, but also their absolute stability regions are considerably larger. Sometimes this fact allows us to apply larger time-stepsizes during the numerical solution when Richardson Extrapolation is used. The possibility to achieve such a positive effect is verified by numerical experiments carried out with a carefully chosen example. It is pointed out that the application of Richardson Extrapolation together with explicit Runge-Kutta methods might be useful when some large-scale mathematical models, including models that are arising in air pollution studies, are handled numerically.
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Acknowledgments
The research of K. Georgiev and I. Dimov is supported in part by Grants DCVP-02/1 and I01/5 from the Bulgarian National Science Found. The authors thanks Centre of Scientific Computing at Technical University of Denmark for giving access to their computers for making computations.
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Zlatev, Z., Georgiev, K., Dimov, I. (2014). Stability Properties of Explicit Runge-Kutta Methods Combined with Richardson Extrapolation. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2013. Lecture Notes in Computer Science(), vol 8353. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43880-0_49
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DOI: https://doi.org/10.1007/978-3-662-43880-0_49
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