Numerical approximation of first kind Volterra convolution integral equations with discontinuous kernels
JOURNAL OF INTEGRAL EQUATIONS AND APPLICATIONS(2016)
Abstract
The cubic “convolution spline” method for first kind Volterra convolution integral equations was introduced in [Convolution spline approximations of Volterra integral equations, J. Integral Equations Appl., 26:369–410, 2014 ]. Here we analyse 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.
MoreTranslated text
Key words
Volterra integral equations,discontinuous kernel,time delay
AI Read Science
Must-Reading Tree
Example
![](https://originalfileserver.aminer.cn/sys/aminer/pubs/mrt_preview.jpeg)
Generate MRT to find the research sequence of this paper
Chat Paper
Summary is being generated by the instructions you defined