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

08/24/2021

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by   Aslanbek Khibiev, et al.

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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 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.