|ŠÁTEK Václav, KUNOVSKÝ Jiří and SZÖLLÖS Alexandr. Explicit and Implicit Taylor Series Solutions of Stiff Systems. MATHMOD VIENNA 2012 - 7th Vienna Conference on Mathematical Modelling. Vienna: ARGE Simulation News, 2012.|
|Original title:||Explicit and Implicit Taylor Series Solutions of Stiff Systems|
|Title (cs):||Řešení tuhých systémů Explicitní a Implicitní Taylorovou řadou|
|Book:||MATHMOD VIENNA 2012 - 7th Vienna Conference on Mathematical Modelling|
|Series:||Report no. S38|
|Publisher:||ARGE Simulation News|
Dynamic modelling, Numerical solution of differential equations, Stability of numerical methods, Stability domains, Stiff systems, Taylor series methods
The paper deals with stiff systems of differential equations. To solve this sort of system numerically is a diffcult task. In spite of the fact that we come across stiff systems quite often in the common practice, a very interesting and promising numerical method of solving systems of ordinary differential equations (ODE) based on Taylor series has appeared ("Modern Taylor Series Method" (MTSM)).
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 the algorithm using implicit Taylor series - based on recurrent calculation of Taylor series terms and Newton iteration method (ITMRN) is described.