Stoll, MartinYücel, HamdullahMax-Planck-Institut für Dynamik Komplexer Technischer Systeme2025-05-292015https://epflicht.bibliothek.uni-halle.de/handle/123456789/3953870922408urn:nbn:de:gbv:3:2-648042483998Abstract: Fractional differential equations are becoming increasingly popular as a modelling tool to describe a wide range of non-classical phenomena with spatial heterogeneities throughout the applied science and engineering. However, the non-local nature of the fractional operators causes essential difficulties and challenges for numerical approximations. We here address an efficient approach to solve fractional-in-space Allen-Cahn equations via the contour integral method (CIM) for computing the fractional power of a matrix times a vector. Time discretization is performed by the first-and second-order implicit-explicit schemes with an adaptive time-step size approach, whereas spatial discretization is performed by a symmetric interior penalty Galerkin (SIPG) method. Several numerical examples are presented to illustrate the effect of the fractional power.1 Online-Ressource (25 Seiten = 2,21 MB) : Illustrationen, Diagrammeenghttp://rightsstatements.org/vocab/InC/1.0/510Book