Nonlinear stability of one-leg methods for delay differential equations of neutral type

作者：Wang, Wan Sheng^*; Zhang, Yuan; Li, Shou Fu

来源：Applied Numerical Mathematics, 2008, 58(2): 122-130.

DOI：10.1016/j.apnum.2006.11.002

• nonlinear neutral delay differential equations
• one-leg methods
• numerical stability
• A-stability

This paper is devoted to investigations into numerical stability properties of one-leg methods for nonlinear neutral delay differential equations. At first, a series of new stability concepts, such as GS-stability, GAS-stability, and Weak GS-stability, are introduced. Then it is proved that a strongly A-stable one-leg method with linear interpolation is GAS-stable, and that an A-stable one-leg method with linear interpolation is GS-stable and Weakly GS-stable. Some numerical experiments are given in the last section of this paper which confirm our results.

• 出版日期2008-2
• 单位湘潭大学; 长沙学院