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On the asymptotics of the trapezoidal rule for the pantograph equation


Authors: J. Cermák and J. Jánsky
Journal: Math. Comp. 78 (2009), 2107-2126
MSC (2000): Primary 34K28, 39A11; Secondary 65L05, 65L20
DOI: https://doi.org/10.1090/S0025-5718-09-02245-5
Published electronically: March 4, 2009
MathSciNet review: 2521280
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Abstract: The paper deals with the trapezoidal rule discretization of a class of linear delay differential equations, with a special emphasis on equations with a proportional delay. Our purpose is to analyse the asymptotic properties of the numerical solutions and formulate their upper bounds. We also survey the known results and show that our formulae improve and generalize these results. In particular, we set up conditions under which the numerical solution of the scalar pantograph equation has the same decay rate as the exact solution.


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Additional Information

J. Cermák
Affiliation: Institute of Mathematics, Brno University of Technology, Technická 2, CZ-616 69 Brno, Czech Republic
Email: cermak.j@fme.vutbr.cz

J. Jánsky
Affiliation: Institute of Mathematics, Brno University of Technology, Technická 2, CZ-616 69 Brno, Czech Republic
Email: yjansk04@stud.fme.vutbr.cz

DOI: https://doi.org/10.1090/S0025-5718-09-02245-5
Keywords: Pantograph equation, asymptotic behavior, trapezoidal rule
Received by editor(s): December 18, 2007
Received by editor(s) in revised form: November 15, 2008
Published electronically: March 4, 2009
Additional Notes: The authors were supported by the research plan MSM 0021630518 “Simulation modelling of mechatronic systems” of the Ministry of Education, Youth and Sports of the Czech Republic and by the grant # 201/08/0469 of the Czech Grant Agency.
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.