Explicit stabilized Runge–Kutta methods

Explicit Runge–Kutta methods with the stability domains extended along the real axis are examined. For these methods, a simple and efficient procedure for calculating the stability polynomials is proposed. Three techniques for constructing methods with given stability polynomials are considered. Methods of the second and third orders are constructed, and their accuracy as applied to solving the Prothero–Robinson equation is examined. A comparison of the above methods on some test problems is performed.