Current work and open problems in the numerical analysis of Volterra functional equations with vanishing delays
Current work and open problems in the numerical analysis of Volterra functional equations with vanishing delays
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DOI：
10.1007/s11464-009-0001-0
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发表时间：
2009-02
影响因子：
--
通讯作者：
H. Brunner
中科院分区：
文献类型：
--
作者：
H. Brunner
本文的目的是 (i) 综述线性 Volterra 型函数积分和积分微分方程的配置解的超收敛分析的最新进展，其中延迟函数 θ(t) 在积分区间的初始点消失（ia(t) =qt(0 <q< 1,t⩾ 0) 是一个重要的特例），以及 (ii) 通过一系列开放问题指出数值计算中的区域对此类 Volterra 函数方程的分析还需要进行更多研究。
The aims of this paper are (i) to present a survey of recent advances in the analysis of superconvergence of collocation solutions for linear Volterra-type functional integral and integro-differential equations with delay functions θ(t) vanishing at the initial point of the interval of integration (with ia(t) =qt(0 <q< 1,t⩾ 0) being an important special case), and (ii) to point, by means of a list of open problems, to areas in the numerical analysis of such Volterra functional equations where more research needs to be carried out.