Acta mathematica scientia,Series A ›› 2019, Vol. 39 ›› Issue (3): 560-569.

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Asymptotic Estimation of the Trapezoidal Method for a Class of Neutral Differential Equation with Variable Delay

Gengen Zhang1,*(),Wansheng Wang3,Aiguo Xiao2   

  1. 1 School of Mathematics and Statistics, Guangxi Normal University, Guangxi Guilin 541004
    2 School of Mathematics and Computational Science, Xiangtan University, Hunan Xiangtan 411105
    3 Department of Mathematics, Shanghai Normal University, Shanghai 200234
  • Received:2018-02-01 Online:2019-06-26 Published:2019-06-27
  • Contact: Gengen Zhang
  • Supported by:
    the NSFC(11701110)


In this paper, we investigate the stability of the trapezoidal method for a class of neutral differential equation with variable delay and obtain the asymptotic estimation of numerical solution with the aid of a functional inequality. The asymptotic estimation is more accurate than asymptotic stability in describing the behaviours of the numerical solution, and gives the upper bound estimates of the numerical solution for the nonstable case.

Key words: Neutral delay differential equation, Trapezoidal method, Asymptotic estimation, Asymptotic stability

CLC Number: 

  • O241.8