RUS  ENG
Full version
JOURNALS // Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences // Archive

Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2019 Volume 23, Number 3, Pages 582–597 (Mi vsgtu1690)

This article is cited in 5 papers

Short Communication

Stability and convergence of difference schemes for the multi-term time-fractional diffusion equation with generalized memory kernels

A. Kh. Khibiev

Institute of Applied Mathematics and Automation of Kabardin-Balkar Scientific Centre of RAS, Nal’chik, 360000, Russian Federation.

Abstract: In this paper, a priori estimate for the corresponding differential problem is obtained by using the method of the energy inequalities. We construct a difference analog of the multi-term Caputo fractional derivative with generalized memory kernels (analog of L1 formula). The basic properties of this difference operator are investigated and on its basis some difference schemes generating approximations of the second and fourth order in space and the $ (2{-}\alpha_0) $-th order in time for the generalized multi-term time-fractional diffusion equation with variable coefficients are considered. Stability of the suggested schemes and also their convergence in the grid $ L_2 $-norm with the rate equal to the order of the approximation error are proved. The obtained results are supported by numerical calculations carried out for some test problems.

Keywords: fractional derivative, generalized memory kernel, a priori estimates, fractional diffusion equation, finite difference scheme, stability, convergence.

UDC: 519.642.2

MSC: 65M06, 65N06, 65N12

Received: April 16, 2019
Revised: May 25, 2019
Accepted: June 10, 2019
First online: June 21, 2019

DOI: 10.14498/vsgtu1690



Bibliographic databases:


© Steklov Math. Inst. of RAS, 2025