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Numerical investigation of the pantograph equation
Applied Numerical Mathematics, 1997The author studies the stability behaviour of a very simple numerical method when applied to the pantograph equation \[ y'(t)= ay(t)+ by(qt), \qquad|a ...
Yunkang Liu
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Asymptotic stability properties of θ-methods for the pantograph equation
Applied Numerical Mathematics, 1997The authors consider the asymptotic stability properties of \(\theta\)-methods when applied to the pantograph equation \[ y'(t)= ay(t)+ by(qt)+ cy'(qt), \qquad q\in(0,1).\tag{1} \] It is shown that asymptotic stability is obtained when \(\theta>1/2\) for a certain constrained variable stepsize implementation which is characterized by the property that ...
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