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
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.
(m, stiff systems, (m,k)-schemes, Fehlberg method, Runge-Kutta methods, accuracy and stability control, variable structure algorithm, ordinary differential equations, numerical methods.
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E. A. Novikov, “A variable structure algorithm using the (3,2)-scheme and the Fehlberg method”, Num. Meth. Prog., 16:3 (2015), 446–455
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\paper A variable structure algorithm using the (3,2)-scheme and the Fehlberg method
\jour Num. Meth. Prog.
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