Simple difference schemes for multidimensional fractional Laplacian and fractional gradient

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F25%3A00386361" target="_blank" >RIV/68407700:21340/25:00386361 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s13540-025-00386-5" target="_blank" >https://doi.org/10.1007/s13540-025-00386-5</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s13540-025-00386-5" target="_blank" >10.1007/s13540-025-00386-5</a>

Result language
angličtina
Original language name
Simple difference schemes for multidimensional fractional Laplacian and fractional gradient
Original language description
The fractional Laplacian and fractional gradient are operators which play fundamental role in modeling of anomalous diffusion in d-dimensional space with the fractional exponent alpha is an element of(1,2). The principal-value integrals are split into singular and regular parts where we avoid using any weight function for the approximation in the singularity neighborhood. The resulting approximation coefficients are calculated from optimal value of the singular domain radius which is only a function of the exponent alpha and a given grid topology. Various difference schemes are presented for the regular rectangular grids with mesh size h>0, and also for the hexagonal and the dodecahedral ones. This technique enables to evaluate the fractional operators with the approximation error O(h(4-alpha)) which is verified using testing functions with known analytical expression of their fractional Laplacian and fractional gradient. Resulting formulas can be also used for the numeric solution of the fractional partial differential equations.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics

Project
<a href="/en/project/GA21-09093S" target="_blank" >GA21-09093S: Multiphase flow, transport, and structural changes related to water freezing and thawing in the subsurface</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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