Stability and error analysis of one-leg methods for nonlinear delay differential equations

作者：Huang, CM; Li, SF; Fu, HY; Chen, GN

来源：Journal of Computational and Applied Mathematics, 1999, 103(2): 263-279.

DOI：10.1016/S0377-0427(98)00262-3

• nonlinear delay differential equations
• one-leg methods
• stability
• D-convergence

This paper is concerned with the numerical solution of delay differential equations (DDEs). We focus on the stability behaviour and error analysis of one-leg methods with respect to nonlinear DDEs. The new concepts of OR-stability, GAR-stability and weak GAR-stability are introduced. It is proved that a strongly A-stable one-leg method with linear interpolation is GAP-stable, and that an A-stable one-leg method with linear interpolation is GR-stable, weakly CAR-stable and D-convergent of order s, if it is consistent of order a in the classical sense.

• 出版日期1999-3-31
• 单位湘潭大学; 中国工程物理研究院