doc. Ing. Petr Tomášek, Ph.D.
E-mail:   Petr.Tomasek@vut.cz  Dept.:   Institute of Mathematics Position:   Institute Secretary for Educational Activities Room:   A1/1823 Dept.:   Institute of Mathematics Dept. of Mathematical Analysis Position:   Associate Professor Room:   A1/1823

Supervised courses:

• Calculus with MAPLE (0MV)
• Mathematical Software (0MS)
• Numerical Mathematics I (9NM1)
• Numerical Methods (2NU)
• Numerical Methods (2NU-A)
• Numerical Methods I (SN1)
• Numerical Methods II (9NM2)
• Numerical Methods II (SN2)
• Numerical Methods III (SN3)
• Numerical Methods III (SN3-A)

Publications:

• ČERMÁK, J.; TOMÁŠEK, P.:
  On delay-dependent stability conditions for a three-term linear difference equation, Japan Publications Trading Co., Ltd.
  journal article in Web of Science
• TOMÁŠEK, P.:
  An asymptotic estimate for linear delay differential equations with power delayed arguments,
  Advances in Dynamical Systems and Applications (ADSA), Vol.8, (2013), No.2, pp.379-386, ISSN 0973-5321, Research India Publications
  journal article - other
• HRABALOVÁ, J.; TOMÁŠEK, P.:
  On stability regions of the modified midpoint method for a linear delay differential equation, Springer
  journal article in Web of Science
• ČERMÁK, J.; JÁNSKÝ, J.; TOMÁŠEK, P.:
  On necessary and sufficient conditions for the asymptotic stability of higher order linear difference equations,
  JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, Vol.18, (2012), No.11, pp.1781-1800, ISSN 1023-6198, Taylor & Francis
  journal article - other
• KUNDRÁT, P.; JÁNSKÝ, J.:
  The stability analysis of a discretized pantograph equation,
  Mathematica Bohemica, Vol.136, (2011), No.4, pp.385-394, ISSN 0862-7959
  journal article - other
• KUNDRÁT, P.:
  Asymptotic estimate for differential equation with power coefficients and power delays, Mathematical Institute, Slovak Academy of Sciences
  journal article in Web of Science
• KUNDRÁT, P.:
  Discretized pantograph equation with a forcing term: Note on asymptotic estimate,
  DISCRETE DYNAMICS AND DIFFERENCE EQUATIONS Proceedings of the Twelfth International Conference on Difference Equations and Applications, pp.307-312, ISBN 978-981-4287-64-7, (2010), World Scientific Publishing Co.
  conference paper
  akce: The Twelfth International Conference on Difference Equations and Applications (ICDEA 2007), Lisbon, 23.07.2007-27.07.2007

List of publications at Portal BUT

Abstracts of most important papers:

• ČERMÁK, J.; TOMÁŠEK, P.:
  On delay-dependent stability conditions for a three-term linear difference equation, Japan Publications Trading Co., Ltd.
  journal article in Web of Science
  The paper presents a new type of necessary and sufficient conditions for asymptotic stability of a three-term linear delay difference equation. The derived condition are explicit and involve a critical value of delay, when the studied equation loses its asymptotic stability property.
• HRABALOVÁ, J.; TOMÁŠEK, P.:
  On stability regions of the modified midpoint method for a linear delay differential equation, Springer
  journal article in Web of Science
  The paper deals with stability regions of certain discretization of linear differential equation with constant delay. The main aim of the paper is to analyze regions of asymptotic stability of modified midpoint method applied to a linear differential equation with constant delay. Obtained results are compared with other known results, particularly for Euler discretization. There is discussed a relation between asymptotic stability conditions in the discrete case and continuous case, too.
• ČERMÁK, J.; JÁNSKÝ, J.; TOMÁŠEK, P.:
  On necessary and sufficient conditions for the asymptotic stability of higher order linear difference equations,
  JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, Vol.18, (2012), No.11, pp.1781-1800, ISSN 1023-6198, Taylor & Francis
  journal article - other
  This paper discusses two explicit forms of necessary and sufficient conditions for the asymptotic stability of the autonomous four-term linear difference equation. These conditions are derived by use of the Schur–Cohn criterion converted into a more applicable form.
• ČERMÁK, J.; KUNDRÁT, P.; URBÁNEK, M.:
  Delay equations on time scales: Essentials and asymptotics of solutions,
  JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, Vol.14, (2008), No.6, pp.567-580, ISSN 1023-6198, Taylor & Francis
  journal article - other
  The paper deals with basics of the qualitative theory of delay equations on time scales. In particular, we apply our approach to the numerical analysis of some delay differential equations.
• KUNDRÁT, P.:
  Asymptotic properties of solutions of the difference equation \Delta x(t)=-ax(t)+bx(\tau(t)),
  Proceedings of the Eighth International Conference on Difference Equations and Applications, pp.193-200, ISBN 1-58488-536-X, (2005), Chapman & Hall
  conference paper
  akce: 8-th International Conference on Difference Equations and Applications, Brno, 28.07.2003-01.08.2003
  In this paper we derive the asymptotic bounds of all solutions of the delay difference equation \Delta x(t)=-ax(t)+bx(\tau(t)), t\in[t_0,infinity) with real constants a>0, b\neq 0. This equation is obtained via the discretization of a delay differential equation and we show the resemblance in the asymptotic bounds of both equations.