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A Second-Order Difference Scheme for Generalized Time-Fractional Diffusion Equation with Smooth Solutions by Aslanbek Khibiev; Anatoly Alikhanov; Chengming Huang is a Engineering article available to read on EtoBox.

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

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

Author

Aslanbek Khibiev; Anatoly Alikhanov; Chengming Huang

Publisher

Walter de Gruyter GmbH

Published

2023

Language

EN

Field

Engineering (Physical Sciences)