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, RungeòÀÓKutta methods, accuracy and stability control, variable structure algorithm, ordinary differential equations, numerical methods.

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