A Second-Order Difference Scheme for Generalized Time-Fractional Diffusion Equation with Smooth Solutions

Autor:	Aslanbek Khibiev, Anatoly Alikhanov, Chengming Huang
Rok vydání:	2023
Předmět:	Computational Mathematics Numerical Analysis Applied Mathematics
Zdroj:	Computational Methods in Applied Mathematics.
ISSN:	1609-9389 1609-4840
DOI:	10.1515/cmam-2022-0089
Popis:	In the current work, we build a difference analog of the Caputo fractional derivative with generalized memory kernel (𝜇L2-1𝜎 formula). The fundamental features of this difference operator are studied, and on its ground, some difference schemes generating approximations of the second order in time for the generalized time-fractional diffusion equation with variable coefficients are worked out. We have proved stability and convergence of the given schemes in the grid L 2 L_{2} -norm with the rate equal to the order of the approximation error. The achieved results are supported by the numerical computations performed for some test problems.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::11b4651b1bb541ebae9030c841890ec2 https://doi.org/10.1515/cmam-2022-0089 Zobrazit plný text záznamu