L-stability of multi-implicit methods of 8-th order for differential stiff systems

The new set of absolutely stable difference schemes for a numerical solution of ODEs stiff systems (1) is submitted. The main feature of the set is the multi-implicit finite differences with the second derivatives of the desired solution. The expanded two-parameter (a, ß set of 3ISD-schemes (2-3) is studied in more details in this paper. The testing of this difference schemes on linear and non-linear problems with a different stiff power is conducted. The errors of a numerical solution as functions of integration step size are computed in numerical experiments. These results demonstrate high quality of stability and accuracy of the suggested 3ISD-schemes.