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IMA Journal of Applied Mathematics Advance Access published online on October 27, 2009
IMA Journal of Applied Mathematics, doi:10.1093/imamat/hxp029
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© The Author 2009. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Analysis of delay-dependent stability of linear {theta}-methods for linear delay-integro-differential equations

Yang Xu{dagger} and Jing-Jun Zhao

Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China

{dagger} Email: yangx{at}hit.edu.cn

Received on January 3, 2008; Revision received August 6, 2009. Accepted on September 30, 2009

In this paper, the stability regions of linear {theta}-methods are considered with respect to the linear integro-differential equation with an arbitrary but fixed delay. A necessary condition is proved for {theta}-methods to be weakly {tau}(0)-stable and a sufficient condition is conjectured by some numerical investigation.

Keywords: delay-integro-differential equations; numerical methods; delay-dependent stability.


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