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IMA Journal of Numerical Analysis Advance Access originally published online on May 13, 2008
IMA Journal of Numerical Analysis 2009 29(2):444-465; doi:10.1093/imanum/drn011
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© The author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Stability analysis of general linear methods for the nonautonomous pantograph equation

Chengming Huang{dagger}

Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074, China and Scientific Computing Key Laboratory of Shanghai Universities

{dagger} Email: chengming_huang{at}hotmail.com

Received on 15 November 2006. Revised on 16 January 2008.


  Abstract

This paper is concerned with the study of the stability of general linear methods for the nonautonomous pantograph equation. Linear and nonlinear problems are considered separately. We derive the asymptotic stability of numerical methods with strict stability at infinity for neutral equations. Also, we obtain some bounds for the error growth for algebraically stable methods applied to non-neutral equations.

Key Words: pantograph equation; general linear methods; asymptotic stability; boundedness stability


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