Stability criteria for exact and discrete solutions of neutral multidelay-integro-differential equations
Stability criteria for exact and discrete solutions of neutral multidelay-integro-differential equations
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DOI：
10.1007/s10444-007-9037-4
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发表时间：
2008-05
影响因子：
1.7
通讯作者：
Chengjian Zhang;S. Vandewalle
中科院分区：
文献类型：
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作者：
Chengjian Zhang;S. Vandewalle
研究中立型多时滞积分微分方程精确解和离散解的渐近稳定性。给出了保证精确解渐近稳定的充分条件。提出了经典龙格-库塔法和线性多步法的自适应解这类具有等时滞的系统。对这些数值方法的渐近稳定性构造了稳定性判据，并与连续问题的稳定性判据进行了比较。结果表明，在适当的条件下，这两类数值方法都能保持连续系统的稳定性。给出了一些数值算例来验证理论结果。
This paper deals with the asymptotic stability of exact and discrete solutions of neutral multidelay-integro-differential equations. Sufficient conditions are derived that guarantee the asymptotic stability of the exact solutions. Adaptations of classical Runge–Kutta and linear multistep methods are suggested for solving such systems with commensurate delays. Stability criteria are constructed for the asymptotic stability of these numerical methods and compared to the stability criteria derived for the continuous problem. It is found that, under suitable conditions, these two classes of numerical methods retain the stability of the continuous systems. Some numerical examples are given that illustrate the theoretical results.