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Num. Meth. Prog., 2015, Volume 16, Issue 3, Pages 446–455 (Mi vmp554)  

A variable structure algorithm using the (3,2)-scheme and the Fehlberg method

E. A. Novikov

Institute of Computational Modelling, Siberian Branch of the Russian Academy of Sciences, Krasnoyarsk

Abstract: A third-order (3,2)-method allowing freezing the Jacobi matrix is constructed. Its main and intermediate numerical schemes are $L$-stable. An accuracy control inequality is obtained using an embedded method of second order. A stability control inequality for the explicit three-stage Runge-Kutta-Fehlberg method of third order is proposed. A variable structure algorithm is formulated. An explicit or $L$-stable method is chosen according to the stability criterion at each step. Numerical results are discussed.

Keywords: (m, stiff systems, (m,k)-schemes, Fehlberg method, Runge-Kutta methods, accuracy and stability control, variable structure algorithm, ordinary differential equations, numerical methods.

Full text: PDF file (216 kB)
UDC: 519.622
Received: 16.06.2015

Citation: E. A. Novikov, “A variable structure algorithm using the (3,2)-scheme and the Fehlberg method”, Num. Meth. Prog., 16:3 (2015), 446–455

Citation in format AMSBIB
\Bibitem{Nov15}
\by E.~A.~Novikov
\paper A variable structure algorithm using the (3,2)-scheme and the Fehlberg method
\jour Num. Meth. Prog.
\yr 2015
\vol 16
\issue 3
\pages 446--455
\mathnet{http://mi.mathnet.ru/vmp554}


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