Analysis of collocation solutions for a class of functional equations with vanishing delays
Analysis of collocation solutions for a class of functional equations with vanishing delays
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DOI：
10.1093/imanum/drp051
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发表时间：
2011-04
影响因子：
2.1
通讯作者：
H. Brunner;Hehu Xie;Ran Zhang
中科院分区：
文献类型：
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作者：
H. Brunner;Hehu Xie;Ran Zhang
研究了时滞函数方程y（t）=B（t）y（θ（t））+f（t），t∈ [0，T]解的存在唯一性和正则性，其中时滞函数θ（t）为零att= 0.对应于线性延迟函数θ（t）=qt（0 <q< 1）的函数方程是一个重要的特例。然后，我们分析的最佳顺序的分段多项式配置逼近这些功能方程的解决方案的收敛性。通过大量的数值例子说明了理论结果。
We study the existence, uniqueness and regularity properties of solutions for the functional equationy(t) =b(t)y(θ(t)) +f(t),t∈ [0,T], where the delay functionθ(t) vanishes att= 0. Functional equations corresponding to the linear delay functionθ(t) =qt(0 <q< 1) represent an important special case. We then analyse the optimal order of convergence of piecewise polynomial collocation approximations to solutions of these functional equations. The theoretical results are illustrated by extensive numerical examples.