Dissipativity of extended Pouzet–Runge–Kutta methods for neutral delay integro-differential equations

Abstract

This paper is concerned with dissipativity of extended Pouzet–Runge–Kutta methods for neutral delay integro-differential equations. The finite-dimensional and infinite-dimensional dissipativity results of the (k, l)-algebraically stable extended Pouzet–Runge–Kutta methods are obtained under suitable conditions.

Keywords:

• neutral delay integro-differential equations
• (k, l)-algebraical stability
• extended Pouzet–Runge–Kutta methods
• finite-dimensional dissipativity
• infinite-dimensional dissipativity

2000 AMS Subject Classifications::

• 65L05
• 65L06
• 65L20

Acknowledgements

The authors are indebted to the referees and the editors for their careful reading of this paper and their valuable comments. This work was supported by NSF of China (Nos. 91130003, 11371157 and 11326240), the Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan) (No. CUG120828) and the Special Fund for Basic Scientific Research of Central Colleges, China University of Geosciences (Wuhan) (No. CUGL130247).