Detail publikace

# Stiff Systems Analysis

Originální název

Stiff Systems Analysis

Anglický název

Stiff Systems Analysis

Jazyk

en

Originální abstrakt

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.

Anglický abstrakt

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.

BibTex

``````
@article{BUT97050,
author="Václav {Šátek}",
title="Stiff Systems Analysis",
annote="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.",