Asymptotic stability, contractivity and dissipativity of one-leg theta-method for non-autonomous delay functional differential equations

作者：Tian Hongjiong^*; Guo Ni

来源：Applied Mathematics and Computation, 2008, 203(1): 333-342.

DOI：10.1016/j.amc.2008.04.045

• asymptotic stability
• contractivity
• dissipativity
• delay functional differential equation
• one-leg theta-method

This paper focuses on asymptotic stability, contractivity and dissipativity of non-autonomous nonlinear delay functional differential equations with bounded lag, and the corresponding dynamical properties of one-leg theta-method. Sufficient conditions for these delay functional differential equations to be dissipative, asymptotically stable and contractive are established. One-leg theta-method is constructed to solve such equations numerically. An important result on the growth of solution of a class of difference inequalities with variable coefficients is obtained. Finally, it is proved that the one-leg h-method is asymptotically stable, contractive and dissipative if and only if theta = 1. Numerical examples are given to confirm our theoretical results.

• 出版日期2008-9-1
• 单位上海大学; 上海师范大学