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

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

  • Novikov E.A. – Institute of Computational Modeling, Siberian Branch of Russian Academy of Sciences; Akademgorodok 50/44, Krasnoyarsk, 660036, Russia; Dr. Sci., Professor, Principal Scientist, e-mail: novikov@icm.krasn.ru