Oscillations analysis of numerical solutions for neutral delay differential equations

Abstract

In this paper, we will study oscillations of numerical solutions for the neutral delay differential equation

where p∈ℝ and p≠0, τ, q∈(0,+∞), σ≥0. Conditions under which numerical solutions of the above differential equation are oscillatory are obtained. The condition that leads to oscillations of the linear θ-method is also given. To verify our results, we give numerical experiments.

Keywords:

• oscillation
• neutral
• delay differential equations
• numerical method

2000 AMS Subject Classifications :

• 34C10
• 39B72
• 74S99

Acknowledgements

This work is supported by the Educational Department Scientific Technology Program of Heilongjiang Province (11551136), Academic Foundation for Youth of Harbin Normal University (KJB200816, 10KXQ_05) and Science Fund for Young of Heilongjiang Province (QC2010036).