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Open Computer Science

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Model of the telegraph line and its numerical solution

Petr Veigend
  • Corresponding author
  • Brno University of Technology, Faculty of Information Technology, Božetěchova 2, 612 66, Brno, Czech Republic
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Gabriela Nečasová
  • Brno University of Technology, Faculty of Information Technology, Božetěchova 2, 612 66, Brno, Czech Republic
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Václav Šátek
  • Brno University of Technology, Faculty of Information Technology, Božetěchova 2, 612 66, Brno, Czech Republic
  • IT4Innovations, VŠB Technical University of Ostrava, 17. listopadu 15/2172, 708 33, Ostrava-Poruba, Czech Republic
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2018-06-28 | DOI: https://doi.org/10.1515/comp-2018-0002

Abstract

This paper deals with a model of the telegraph line that consists of system of ordinary differential equations, rather than partial differential telegraph equation. Numerical solution is then based on an original mathematical method. This method uses the Taylor series for solving ordinary differential equations with initial condition - initial value problems in a non-traditional way. Systems of ordinary differential equations are solved using variable order, variable step-size Modern Taylor Series Method. The Modern Taylor Series Method is based on a recurrent calculation of the Taylor series terms for each time interval. The second part of paper presents the solution of linear problems which comes from the model of telegraph line. All experiments were performed using MATLAB software, the newly developed linear solver that uses Modern Taylor Series Method. Linear solver was compared with the state of the art solvers in MATLAB and SPICE software.

Keywords: Telegraph line; ordinary differential equations; Taylor series method; MATLAB; SPICE

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About the article

Received: 2018-02-28

Accepted: 2018-04-25

Published Online: 2018-06-28


Citation Information: Open Computer Science, Volume 8, Issue 1, Pages 10–17, ISSN (Online) 2299-1093, DOI: https://doi.org/10.1515/comp-2018-0002.

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© 2018 Petr Veigend, et al., published by De Gruyter. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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