Stiff Systems Analysis

Stiff Systems of Differential Equations, Taylor Series Method, Ordinary Differential Equations, Initial Value Problems, Numerical Solutions of Differential Equations, TKSL software

The paper deals with stiff systems of differential equations. To solve this sort of system numerically is a diffult task. In spite of the fact that we come across stiff systems quite often in the common practice, a very interesting and promissing numerical method of solving systems of ordinary differential equations (ODE) based on Taylor series has appeared. The question was how to harness the said "Modern Taylor Series Method" (MTSM) for solving of stiff systems.

The potential of the Taylor series has been exposed by many practical experiments and a way of detection and explicit solution of large systems of ODE has been found. Detailed analysis of stability and convergence of explicit and implicit Taylor series is presented and a new algorithm using implicit Taylor series based on recurrent calculation of Taylor series terms and Newton iteration method (ITMRN) is described. The new method reducing stiffness in system based on finding new equivalent system of ODE "without stiffness" is introduced.