Geodesic
The stability analysis of a discretized pantograph equation
Mathematica Bohemica, Tome 136 (2011) no. 4, pp. 385-394
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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.
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.
DOI : 10.21136/MB.2011.141698
Classification : 34K28, 39A06, 39A12, 39A30, 65L03, 65L05, 65L12, 65L20
Keywords: pantograph equation; numerical solution; stability 
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Jánský, Jiří; Kundrát, Petr. The stability analysis of a discretized pantograph equation. Mathematica Bohemica, Tome 136 (2011) no. 4, pp. 385-394. doi: 10.21136/MB.2011.141698

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