Stability of two-step Runge–Kutta methods for neutral delay differential-algebraic equations

Abstract

This paper develops the two-step Runge–Kutta methods (TSRKs) for the neutral delay differential-algebraic equations (NDDAEs) and proves that the TSRKs are asymptotically stable for linear NDDAEs under the assumption that the coefficient matrices are all upper triangular, which is necessary to formulate the stability result. The discussions are supported by the numerical experiments.

Keywords:

• asymptotic stability
• neutral delay differential-algebraic equations
• two-step Runge–Kutta methods

2000 AMS Subject Classification :

• 34A34

Acknowledgement

The work is supported in part by the Scientific Computing Key Laboratory of Shanghai University and the Shanghai Leading Academic Discipline Project (No.S30405).