Stability of ROW methods for non autonomous systems of ordinary differential equations

Studying of $AN$-stability of $ROW$ methods has been done. Notion of $LN$-equivalence of difference schemes are introduced. Possibilities of construction of schemes with better stability properties for the linear non autonomous and nonlinear problems has been studied with the use of algebraically stable singly diagonally-implicit Runge–Kutta ($SDIRK$) methods. The impossibility of construction of $LN$-stable $ROW$ methods for numerical integration of stiff systems of ODE which are based on $SDIRK$ schemes is shown.