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


  • E.A. Novikov Institute of Computational Modeling of SB RAS (ICM SB RAS)




stiff systems, k)-schemes, Fehlberg method, Runge–Kutta methods, accuracy and stability control, variable structure algorithm, ordinary differential equations, numerical methods


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.

Author Biography

E.A. Novikov


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How to Cite

Новиков Е. A Variable Structure Algorithm Using the (3,2)-Scheme and the Fehlberg Method // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2015. 16. 446-455. doi 10.26089/NumMet.v16r342



Section 1. Numerical methods and applications