Asymptotic stability of multistep methods for nonlinear delay differential equations

作者：Huang; Chengming

来源：Applied Mathematics and Computation, 2008, 203(2): 908-912.

DOI：10.1016/j.amc.2008.04.003

• delay differential equations
• linear multistep methods
• one-leg methods
• asymptotic stability

This paper is concerned with the numerical solution of delay differential equations. The emphasis is on the nonlinear stability of multistep methods. It is shown that every A-stable linear multistep method with piecewise constant or linear interpolation can preserve the asymptotic stability of a class of nonlinear systems, which is an extension of the well known GP-stability result to the nonlinear case. As a comparison, it is also proved that strict stability at infinity is necessary to the asymptotic stability of one-leg methods for non-autonomous equations.

• 出版日期2008-9-15
• 单位华中科技大学; 湘潭大学