Simple difference schemes for multidimensional fractional Laplacian and fractional gradient

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Simple difference schemes for multidimensional fractional Laplacian and fractional gradient

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Simple difference schemes for multidimensional fractional Laplacian and fractional gradient

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GA21-09093S" target="_blank" >GA21-09093S: Vícefázové proudění, transport a změny struktury zeminy související se zamrzáním a rozmrzáním vody v podpovrchových vrstvách</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Fractional Calculus and Applied Analysis

ISSN

1311-0454

e-ISSN

1314-2224

Svazek periodika

28

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

35

Strana od-do

656-690

Kód UT WoS článku

001449442700001

EID výsledku v databázi Scopus

2-s2.0-105000548221