NUMERICAL APPROXIMATION OF FIRST KIND VOLTERRA CONVOLUTION INTEGRAL EQUATIONS WITH DISCONTINUOUS KERNELS

被引：10

作者：

Davies, Penny J. ^{[1
]}

Duncan, Dugald B. ^{[2
]}

机构：

[1] Univ Strathclyde, Dept Math & Stat, 26 Richmond St, Glasgow G1 1XH, Lanark, Scotland

[2] Heriot Watt Univ, Maxwell Inst Math Sci, Dept Math, Edinburgh EH14 4AS, Midlothian, Scotland

来源：

JOURNAL OF INTEGRAL EQUATIONS AND APPLICATIONS | 2017年 / 29卷 / 01期

关键词：

Volterra integral equations; discontinuous kernel; time delay;

D O I：

10.1216/JIE-2017-29-1-41

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The cubic "convolution spline" method for first kind Volterra convolution integral equations was introduced in P.J. Davies and D.B. Duncan, Convolution spline approximations of Volterra integral equations, Journal of Integral Equations and Applications 26 (2014), 369-410. Here, we analyze its stability and convergence for a broad class of piecewise smooth kernel functions and show it is stable and fourth order accurate even when the kernel function is discontinuous. Key tools include a new discrete Gronwall inequality which provides a stability bound when there are jumps in the kernel function and a new error bound obtained from a particular B-spline quasi-interpolant.

引用

页码：41 / 73

页数：33

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