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Volume 25, Issue 1
Exact and Discretized Dissipativity of the Pantograph Equation

Siqing Gan

J. Comp. Math., 25 (2007), pp. 81-88.

Published online: 2007-02

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  • Abstract

The analytic and discretized dissipativity of nonlinear infinite-delay systems of the form $x'(t)=g(x(t),x(qt)) (q\in (0,1),t›0)$ is investigated. A sufficient condition is presented to ensure that the above nonlinear system is dissipative. It is proved that the backward Euler method inherits the dissipativity of the underlying system. Numerical examples are given to confirm the theoretical results.

  • Keywords

Infinite delay, Pantograph equation, Backward Euler method, Dissipativity.

  • AMS Subject Headings

65L05.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-25-81, author = {Siqing Gan}, title = {Exact and Discretized Dissipativity of the Pantograph Equation}, journal = {Journal of Computational Mathematics}, year = {2007}, volume = {25}, number = {1}, pages = {81--88}, abstract = {

The analytic and discretized dissipativity of nonlinear infinite-delay systems of the form $x'(t)=g(x(t),x(qt)) (q\in (0,1),t›0)$ is investigated. A sufficient condition is presented to ensure that the above nonlinear system is dissipative. It is proved that the backward Euler method inherits the dissipativity of the underlying system. Numerical examples are given to confirm the theoretical results.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8674.html} }
TY - JOUR T1 - Exact and Discretized Dissipativity of the Pantograph Equation AU - Siqing Gan JO - Journal of Computational Mathematics VL - 1 SP - 81 EP - 88 PY - 2007 DA - 2007/02 SN - 25 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8674.html KW - Infinite delay, Pantograph equation, Backward Euler method, Dissipativity. AB -

The analytic and discretized dissipativity of nonlinear infinite-delay systems of the form $x'(t)=g(x(t),x(qt)) (q\in (0,1),t›0)$ is investigated. A sufficient condition is presented to ensure that the above nonlinear system is dissipative. It is proved that the backward Euler method inherits the dissipativity of the underlying system. Numerical examples are given to confirm the theoretical results.

Siqing Gan. (2007). Exact and Discretized Dissipativity of the Pantograph Equation. Journal of Computational Mathematics. 25 (1). 81-88. doi:
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