Stability analysis of extended block boundary value methods for linear neutral delay integro-differential equations

Abstract

This paper is concerned with the stability of extended block boundary value methods (B₂VMs) for the linear neutral delay integro-differential-algebraic equations (NDIDAEs) and the linear neutral delay integro-differential equations (NDIDEs). It is proved that every A-stable B₂VM can preserve the asymptotic stability of the exact solution of NDIDAEs under some certain conditions. A necessary and sufficient condition of the B₂VMs to be asymptotically stable for NDIDEs is also obtained. A few numerical experiments confirm the expected results.

Keywords:

• delay integro-differential equations
• delay differential-algebraic equations
• block boundary value methods
• reducible quadrature rules
• asymptotic stability

2000 AMS Subject Classification:

• 65L20

Acknowledgements

The authors wish to thank the two anonymous referees for their valuable comments which helped us to improve the present paper. This work was supported by National Natural Science Foundation of China (11101109, 11271102) and Natural Science Foundation of Hei-long-jiang Province (A201107).