Jiří Janský, Faculty of Mechanical Engineering, Brno University of Technology, Technická 2, Brno, 616 69, Czech Republic, e-mail: yjansk04@stud.fme.vutbr.cz; Petr Tomášek (Kundrát), Faculty of Mechanical Engineering, Brno University of Technology, Technická 2, Brno, 616 69, Czech Republic, e-mail: tomasek@fme.vutbr.cz
Abstract: The paper deals with a difference equation arising from the scalar pantograph equation via the backward Euler discretization. A case when the solution tends to zero but after reaching a certain index it loses this tendency is discussed. We analyse this problem and estimate the value of such an index. Furthermore, we show that the utilized proof technique enables us to investigate some other numerical formulae, too.
Keywords: pantograph equation, numerical solution, stability
Classification (MSC 2010): 39A06, 39A12
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