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- W4285331077 abstract "Two of the most famous definitions of fractional derivatives are the Riemann-Liouville and the Caputo ones. In principle, these formulations are not equivalent and ask for different levels of regularity of the considered function. By focusing on a B-spline collocation discretization of both kind of derivatives, we show that when the fractional order α ranges in (1, 2) their difference in terms of matrices corresponds to a rank-1 correction whose spectral norm increases with the mesh-size n and is ( $$o(sqrt n )$$ ). On one hand, this implies that the spectral distribution for the B-spline collocation matrices corresponding to the Riemann-Liouville and Caputo derivatives coincide; on the other hand, the presence of the rank-1 correction makes the Caputo matrices worse conditioned for α tending to 1 due to a larger maximum singular value. Some linear algebra consequences of all this knowledge are discussed, and a selection of numerical experiments that validate our findings is provided." @default.
- W4285331077 created "2022-07-14" @default.
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- W4285331077 date "2021-11-22" @default.
- W4285331077 modified "2023-09-30" @default.
- W4285331077 title "B-Spline Collocation Discretizations of Caputo and Riemann-Liouville Derivatives: A Matrix Comparison" @default.
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- W4285331077 doi "https://doi.org/10.1515/fca-2021-0072" @default.
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