Stability analysis of block boundary value methods for neutral pantograph equation
Stability analysis of block boundary value methods for neutral pantograph equation
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DOI：
10.1080/10236198.2012.733703
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发表时间：
2013-08
影响因子：
1.1
通讯作者：
Yang Xu;Jing-jun Zhao;Zhenghui Gao
中科院分区：
文献类型：
--
作者：
Yang Xu;Jing-jun Zhao;Zhenghui Gao
研究了中立型比例方程块边值方法的收敛性和稳定性。由于其无界的时间滞后和有限的计算机内存，在独立变量的变化被用来转换成一个非自治的微分方程，具有常数延迟，但可变系数的比例尺方程。证明了在经典Lipschitz条件下，当边界值方法与p阶一致时，BBVM是p阶收敛的，并在一定条件下证明了BBVM能保持中立型比例方程精确解的渐近稳定性.同时，通过数值实验验证了本文的主要结论.
This paper deals with the convergence and stability properties of block boundary value methods (BBVMs) for the neutral pantograph equation. Due to its unbounded time lags and limited computer memory, a change in the independent variable is used to transform a pantograph equation into a non-autonomous differential equation with a constant delay but variable coefficients. It is shown under the classical Lipschitz condition that a BBVM is convergent of order p if the underlying boundary value method is consistent with order p. Furthermore, it is proved under a certain condition that BBVMs can preserve the asymptotic stability of exact solutions for the neutral pantograph equation. Meanwhile, some numerical experiments are given to confirm the main conclusions.