Stiff Systems Analysis

The paper deals with sti systems of dierential equa-tions. To solve this sort of system numerically is a diulttask. In spite of the fact that we come across sti systemsquite often in the common practice, a very interesting andpromissing numerical method of solving systems of ordi-nary dierential equations (ODE) based on Taylor serieshas appeared. The question was how to harness the said"Modern Taylor Series Method" (MTSM) for solving ofsti systems.The potential of the Taylor series has been exposed bymany practical experiments and a way of detection andexplicit solution of large systems of ODE has been found.Detailed analysis of stability and convergence of explicitand implicit Taylor series is presented and a new algo-rithm using implicit Taylor series based on recurrent cal-culation of Taylor series terms and Newton iteration me-thod (ITMRN) is described. The new method reducingstiness in system based on nding new equivalent systemof ODE without stiness" is introduced.