Jan Čermak, Brno University of Technology, Csehország) szemináriumi előadást tart a Matematika Tanszéken.
Pannon Egyetem Matematika Tanszékének és a VEAB Matematikai és Fizikai Szakbizottsága Matematikai Analízis és Alkalmazási Munkabizottságának szervezésében
Prof. Jan Čermak
Brno University of Technology, Csehország
2010. november 30. (kedd) 12:15 órakor
Stability and asymptotic properties of the discretized pantograph equation: a uniform mesh versus a quasi-geometric mesh
címmel előadást tart a Pannon Egyetem Matematika Tanszék Könyvtárában (Veszprém, Egyetem utca 10., E épület, földszint)
Abstract. This contribution discusses and analyzes a numerical solution of the delay di erential equation
y'(t) = a y(t) + b y(qt), t ≥ 0
(usually referred to as the pantograph equation), where a, b are nonzero complex numbers and 0 < q < 1 is a real number. We give a brief review of the equation's basic stability and asymptotic properties and analyze these characteristics for its Θ-methods discretizations. Doing this, we consider the corresponding Θ-method on a mesh with a constant stepsize (which is essentially a di erence equation of in nite order) as well as on a mesh with a speci c variable stepsize (giving rise to a special fi nite order Poincare di erence equation). Further, we discuss the consequences of our results for numerical investigations of the pantograph equation, especially with respect to a possible correspondence between the asymptotics of exact and numerical solutions. Some illustrating examples, calculations and comparisons will be presented as well.
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