Variable order and step algorithm based on a stages of Runge–Kutta method of third order of accuracy

An inequality for the stability control of 3-stage Runge–Kutta method of 3th order of accuracy is obtained. Method of first order with expanded stability domain is constructed. Algorithm of variable order is formulated. The results of stiff system computations are provided, which confirm an increase in efficiency for the variable order method as compared to a calculation with fixed scheme.