Asymptotic stability of general linear methods for systems of linear neutral delay differential-algebraic equations

Abstract

This paper is concerned with numerical stability of general linear methods (GLMs) for a system of linear neutral delay differential-algebraic equations. A sufficient and necessary condition for asymptotic stability of GLMs solving such system is derived. Based on this main result, we further investigate the asymptotic stability of linear multistep methods, Runge–Kutta methods, and block θ-methods, respectively. Numerical experiments confirm our theoretical result.

Keywords:

• neutral delay differential-algebraic equation
• asymptotic stability
• general linear methods
• strong A-stability
• numerical stability

2010 AMS Subject Classifications::

• 65L06
• 65L20
• 65L80

Acknowledgements

The authors are grateful to the referees for their helpful suggestions and valuable comments. The work of Q. Yu is supported by Doctoral Research Fund of Shanghai Ocean University. The work of H. Tian is supported in part by E-Institutes of Shanghai Municipal Education Commission (No. E03004), NSF of China (No. 11071170), Ministry of Education of China (No. 211058), Specialized Research Fund for the Doctoral Program of Higher Education (No. 20113127110003) and Shanghai Municipal Education Commission (No. 11ZZ118).