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- W2945705135 abstract "The paper considers the problem of finite-difference simulation of filtration processes on the base of a space-fractional-differential equation with a generalised Caputo derivative with respect to a function. To make calculations faster, we propose an algorithm of fractional derivative approximation which reduces the computational complexity of matrix operations that arise while performing simulations on uniform and non-uniform grids. The algorithm is based on Taylor’s series expansions of fractional integral kernel and special representation of the matrices of linear systems that arise during finite-difference approximation. Theoretical estimates of the proposed algorithm’s complexity and accuracy are presented. We describe and experimentally compare computational schemes for matrix-vector multiplication used for numerical solution of linear systems by the BicgStab algorithm and analyse factors that influence its convergence. The results of computational experiments which demonstrate an efficiency of the proposed computational scheme for solving a filtration equation with a generalised Caputo derivative with respect to a space variable on a large-sized grids are given." @default.
- W2945705135 created "2019-05-29" @default.
- W2945705135 creator A5077513551 @default.
- W2945705135 date "2019-05-20" @default.
- W2945705135 modified "2023-09-27" @default.
- W2945705135 title "A fast finite-difference algorithm for solving space-fractional filtration equation with a generalised Caputo derivative" @default.
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- W2945705135 doi "https://doi.org/10.1007/s40314-019-0878-5" @default.
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