Conference paperNEČASOVÁ Gabriela, VEIGEND Petr and ©ÁTEK Václav. Modern Taylor series method in numerical integration: PART 2. In: 17th CzechPolish Conference Modern Mathematical Methods in Engineering (3mi). Horní Lomná: V©B  Technical University of Ostrava, 2018, pp. 211220. ISBN 9788024841359.  Publication language:  english 

Original title:  Modern Taylor series method in numerical integration: PART 2 

Pages:  211220 

Proceedings:  17th CzechPolish Conference Modern Mathematical Methods in Engineering (3mi) 

Conference:  Modern Mathematical Methods in Engineering 

Place:  Horní Lomná, CZ 

Year:  2018 

ISBN:  9788024841359 

Publisher:  V©B  Technical University of Ostrava 

Keywords 

Taylor series method, ordinary differential equations, technical initial value problems 
Annotation 

The paper deals with extremely exact, stable, and fast numerical solutions of systems of differential equations with initial condition  initial value problems. Systems of ordinary differential equations are solved using variable order, variable stepsize Modern Taylor Series Method. The Modern Taylor Series Method is based on a recurrent calculation of the Taylor series terms for each time interval. Thus, the complicated calculation of higher order derivatives (much criticized in the literature) need not be performed but rather the value of each Taylor series term is numerically calculated. The paper present the solution of linear and nonlinear problems. As a linear problem, the telegraph equation was chosen. As a nonlinear problem, the behavior of Lorenz system was analyzed. All experiments were performed using MATLAB software, the newly developed nonlinear solver that uses Modern Taylor Series Method was used. Both linear and nonlinear solvers were compared with state of the art solvers in MATLAB. 
BibTeX: 

@INPROCEEDINGS{
author = {Gabriela Ne{\v{c}}asov{\'{a}} and Petr Veigend and
V{\'{a}}clav {\v{S}}{\'{a}}tek},
title = {Modern Taylor series method in numerical
integration: PART 2},
pages = {211220},
booktitle = {17th CzechPolish Conference Modern Mathematical Methods in
Engineering (3mi)},
year = {2018},
location = {Horn{\'{i}} Lomn{\'{a}}, CZ},
publisher = {V{\v{S}}B  Technical University of Ostrava},
ISBN = {9788024841359},
language = {english},
url = {http://www.fit.vutbr.cz/research/view_pub.php?id=11639}
} 
