A second order difference scheme for time fractional diffusion equation with generalized memory kernel

2021/08/24 by Aslanbek Khibiev, Anatoly A. Alikhanov, Khibiev, Aslanbek +3
Mathematics · #Fractional Differential Equations Solutions #Differential Equations and Numerical Methods #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.2108.10596

Abstract

In the current work we build a difference analog of the Caputo fractional derivative with generalized memory kernel (_λL2-1_σ 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 L₂ - 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.

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