Fractional differential problems with numerical anti-reflective boundary conditions: a computational/precision analysis and numerical results
| Autor: | Sousa, Ercília, Tablino-Possio, Cristina, Krause, Rolf, Serra-Capizzano, Stefano |
|---|---|
| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Twenty years ago the anti-reflective numerical boundary conditions (BCs) were introduced in a context of signal processing and imaging, for increasing the quality of the reconstruction of a blurred signal/image contaminated by noise and for reducing the overall complexity to that of few fast sine transforms i.e. to $O(N\log N)$ real arithmetic operations, where $N$ is the number of pixels. Here for quality of reconstruction we mean a better accuracy and the elimination of boundary artifacts, called ringing effects. Now we propose numerical anti-reflective BCs in the context of nonlocal problems of fractional differential type: the goals are the same i.e. a smaller approximation error and the reduction of boundary artifacts. In the latter setting, we compare various types of numerical BCs, including the anti-symmetric ones considered in the case of fractional differential problems for modeling reasons. More in detail, given important similarities between anti-symmetric and anti-reflective BCs, we compare them from the perspective of computational efficiency, by considering nontruncated and truncated versions and also other standard numerical BCs such as reflective/Neumann. Several numerical tests, tables, and visualizations are provided and critically discussed. The conclusion is that the truncated numerical anti-reflective BCs perform better, both in terms of accuracy and low computational cost. Comment: 33 pages, 11 figures |
| Databáze: | arXiv |
| Externí odkaz: |
|