Stable numerical schemes for time-fractional diffusion equation with generalized memory kernel

Autor:	Anatoly A. Alikhanov, Nikki Kedia, Vineet Kumar Singh
Rok vydání:	2022
Předmět:	Computational Mathematics Numerical Analysis Discretization Applied Mathematics Kernel (statistics) Norm (mathematics) Convergence (routing) Applied mathematics Polygon mesh Diffusion (business) Grid Stability (probability) Mathematics
Zdroj:	Applied Numerical Mathematics. 172:546-565
ISSN:	0168-9274
DOI:	10.1016/j.apnum.2021.11.006
Popis:	The paper aims to develop the stable numerical schemes for generalized time-fractional diffusion equations (GTFDEs) with smooth and non-smooth solutions on the non-uniform grid. In time, the generalized Caputo derivative is discretized by a difference scheme of order ( 2 − α ) on a non-uniform grid where 0 α 1 . Choosing the non-uniform meshes in the case of the smooth and non-smooth solution is also essential, so we graded the mesh in both cases separately. Stability and convergence for smooth as well as non-smooth solutions are obtained in L 2 -norm and L ∞ -norm respectively. Several numerical results are presented to show how the grading of meshes is essential. Also, numerical results validate the efficiency and effectiveness of proposed schemes and show how a non-uniform grid produces better results.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::096d94caca7929bf5715614cce9a3ecd https://doi.org/10.1016/j.apnum.2021.11.006 Zobrazit plný text záznamu Full Text from ScienceDirect