Numerical study of one-step lineary implicit methods which are L-equivalent to stiffly accurate two-stages Runge–Kutta schemes

One step free of iterations methods for numerical solution of Cauchy problem for ordinary differential systems of equations there are described. They are equivalent to stiffly accurate 2-stages Runge–Kutta schemes for linear problems (autonomous as well as non-autonomous). Stiff tests such as autonomous Kaps system and non-autonomous Prothero-Robinson problem have been used for numerical study of methods accuracy.