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.

UDC: 519.622

Received: 16.06.2015