<div class="csl-bib-body">
<div class="csl-entry">Rieder, A. (2023). Double exponential quadrature for fractional diffusion. <i>Numerische Mathematik</i>, <i>153</i>, 359–410. https://doi.org/10.1007/s00211-022-01342-8</div>
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dc.identifier.issn
0029-599X
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/191011
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dc.description.abstract
We introduce a novel discretization technique for both elliptic and parabolic fractional diffusion problems based on double exponential quadrature formulas and the Riesz-Dunford functional calculus. Compared to related schemes, the new method provides faster convergence with fewer parameters that need to be adjusted to the problem. The scheme takes advantage of any additional smoothness in the problem without requiring a-priori knowledge to tune parameters appropriately. We prove rigorous convergence results for both, the case of finite regularity data as well as for data in certain Gevrey-type classes. We confirm our findings with numerical tests.
en
dc.language.iso
en
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dc.publisher
SPRINGER HEIDELBERG
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dc.relation.ispartof
Numerische Mathematik
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dc.rights.uri
http://creativecommons.org/licenses/by/4.0/
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dc.subject
functional calculus
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dc.subject
sinc quadrature
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dc.subject
a priori analysis
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dc.subject
exponential convergence
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dc.subject
Mittag-Leffler function
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dc.subject
Fractional laplace
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dc.title
Double exponential quadrature for fractional diffusion