An algorithm of variable structure for solving stiff systems based on an explicit and L-stable method

An explicit Runge-Kutta type scheme with extended stability region is developed and an L-stable (m, k)-method of order two's built. An algorithm of variable step and order based on these methods is obtained where the most effective numerical scheme is chosen for each step basing on stability and accuracy control inequality. The results are given that confirm the effectiveness of this algorithm for accuracy of 1 % and below.