Application of explicit methods with extended stability regions for solving stiff problems

An algorithm is developed to determine coefficients of the stability polynomials such that the explicit Runge–Kutta methods have a predetermined shape and size of the stability region. Inequalities for accuracy and stability control are obtained. The impact of the stability control on efficiency of explicit methods to solving stiff problems is shown. Numerical calculations confirm that the three-step method of the first order with extended stability region is more efficient than the traditional three-stage method of the third order.