Numerical approximations of first kind Volterra convolution equations with discontinuous kernels
| Autor: | Dugald B. Duncan, Penny J. Davies |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Overlap–add method
Numerical Analysis Volterra integral equations Applied Mathematics 010102 general mathematics Mathematical analysis 65M12 65R20 Convolution power time delay 01 natural sciences Integral equation Volterra integral equation Circular convolution Convolution 010101 applied mathematics symbols.namesake Gronwall's inequality symbols 0101 mathematics Convolution theorem QA Mathematics discontinuous kernel |
| Zdroj: | J. Integral Equations Applications 29, no. 1 (2017), 41-73 |
| ISSN: | 0897-3962 |
| Popis: | The cubic ``convolution spline'' method for first kind Volterra convolution integral equations was introduced in P.J. Davies and D.B. Duncan, $\mathit {Convolution\ spline\ approximations\ of\ Volterra\ integral\ equations}$, Journal of Integral Equations and Applications \textbf {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. |
| Databáze: | OpenAIRE |
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