Abstract
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.
Original language | English |
---|---|
Pages (from-to) | 41-73 |
Number of pages | 33 |
Journal | Journal of Integral Equations and Applications |
Volume | 29 |
Issue number | 1 |
Early online date | 19 Oct 2016 |
DOIs | |
Publication status | Published - 27 Mar 2017 |
Keywords
- Discontinuous kernel
- Time delay
- Volterra integral equations
ASJC Scopus subject areas
- Numerical Analysis
- Applied Mathematics
Fingerprint
Dive into the research topics of 'Numerical approximation of first kind Volterra convolution integral equations with discontinuous kernels'. Together they form a unique fingerprint.Profiles
-
Dugald Black Duncan
- School of Mathematical & Computer Sciences - Professor
- School of Mathematical & Computer Sciences, Mathematics - Professor
Person: Academic (Research & Teaching)