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Séka, Hippolyte; Assui, Kouassi Richard

Order of the Runge-Kutta method and evolution of the stability region. (English) Zbl 1450.65069

Ural Math. J. 5, No. 2, 64-71 (2019).
Summary: In this article, we demonstrate through specific examples that the evolution of the size of the absolute stability regions of Runge-Kutta methods for ordinary differential equation does not depend on the order of methods.

MSC:

65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations

Keywords:

stability region; Runge-Kutta methods; ordinary differential equations; order of methods
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\textit{H. Séka} and \textit{K. R. Assui}, Ural Math. J. 5, No. 2, 64--71 (2019; Zbl 1450.65069)
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References:

[1] Butcher J.-C., Numerical Methods for Ordinary Differential Equations, 2nd ed., John Wiley & Sons Ltd., 2008, 175 pp. · Zbl 1167.65041
[2] Calvo M., Montijano J. I., Randez L., “A new embedded pair of Runge-Kutta formulas of orders \(5\) and \(6\)”, Comput. Math. Appl., 20:1 (1990), 15-24 · Zbl 0712.65070
[3] Cassity C. R., “The complete solution of the fifth order Runge-Kutta equations”, SIAM J. Numer. Anal., 6:3 (1969), 432-436 · Zbl 0185.41801
[4] Feagin T., “A tenth-order Runge-Kutta method with error estimate”, Proc. of the IAENG Conf. on Scientific Computing, Hong Kong, 2007
[5] Feagin T., High-Order Explicit Runge-Kutta Methods, 2013 · Zbl 1278.65107
[6] Hairer E., Nørsett S. P., Wanner G., Solving Ordinary Differential Equations I. Nonstiff Problems, Springer Ser. Comput. Math., 8, Springer-Verlag, Berlin-Heidelberg, 1993, 528 pp. · Zbl 0789.65048
[7] Houben S., Stability Regions of Runge-Kutta Methods, Eindhoven University of Technology, 2002
[8] Jackiewicz Z., General Linear Methods for Ordinary Differential Equations, John Wiley & Sons Inc., 2009, 482 pp. · Zbl 1211.65095
[9] Khashin S. I., List of Some Known Runge-Kutta Methods Family, Preliminary version, 2013
[10] Kashin S. I., “Estimating the error in classical Runge-Kutta methods”, Comput. Math. Math. Phys., 54:5 (2014), 767-774 · Zbl 1313.65207
[11] Liu M.Ż., Song M. H., Yang Z. W., “Stability of Runge-Kutta methods in the numerical solution of equation \(u''(t)=au(t)+a_0u([t])\)”, J. Comput. Appl. Math., 166:2 (2004), 361-370 · Zbl 1052.65070
[12] Seka H., Assui K. R., “A New Eighth Order Runge-Kutta Family Method”, J. Math. Res., 11:2 (2019), 190-199
[13] Velagala S. R., Stability Analysis of the 4th order Runge-Kutta Method in Application to Colloidal Particle Interactions, Master’s thesis, University of Illinois, Urbana-Champaign, USA, 2014
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.