Abstract:
The paper is devoted to the development and program implementation of a computational
algorithm for modeling a process of anomalous diffusion. The mathematical model is
formulated as an initial-boundary value problem for a nonlinear fractional order partial
differential equation. An implicit finite-difference scheme based on an increased accuracy order approximation for the Caputo derivative is constructed. An application program was designed to perform computer simulation of the anomalous diffusion process.
The numerical analysis of the accuracy of approximate solutions is conducted using a
test-problem. The results of computational experiments are presented on the example of
the modeling of a fractal nonlinear dynamic reaction-diffusion system.
Citation:
L. I. Moroz, A. G. Maslovskaya, “Numerical simulation of an anomalous diffusion process based on the higher-order accurate scheme”, Mat. Model., 32:10 (2020), 62–76; Math. Models Comput. Simul., 13:3 (2021), 492–501
\Bibitem{MorMas20}
\by L.~I.~Moroz, A.~G.~Maslovskaya
\paper Numerical simulation of an anomalous diffusion process based on the higher-order accurate scheme
\jour Mat. Model.
\yr 2020
\vol 32
\issue 10
\pages 62--76
\mathnet{http://mi.mathnet.ru/mm4223}
\crossref{https://doi.org/10.20948/mm-2020-10-05}
\transl
\jour Math. Models Comput. Simul.
\yr 2021
\vol 13
\issue 3
\pages 492--501
\crossref{https://doi.org/10.1134/S207004822103011X}
Linking options:
https://www.mathnet.ru/eng/mm4223
https://www.mathnet.ru/eng/mm/v32/i10/p62
This publication is cited in the following 10 articles:
L. I. Moroz, A. G. Maslovskaya, “A fractional-differential approach to numerical simulation of electron-induced charging of ferroelectrics”, J. Appl. Industr. Math., 18:1 (2024), 137–149
D. A. Tverdyi, R. I. Parovik, “The optimization problem for determining the functional dependence of the variable order of the fractional derivative of the gerasimov-caputo type”, Vestnik KRAUNC. Fiz.-Mat. Nauki, 47:2 (2024), 35–57
L.I. Moroz, “An Algorithm for the Numerical Solutions of the Time-Space Fractional Reaction-Diffusion-Drift Equation”, Modelling and Data Analysis, 14:3 (2024), 105
Y. V. Slastushenskiy, D. L. Reviznikov, S. A. Semenov, “METHODS FOR PARAMETRIC IDENTIFICATION OF FRACTIONAL DIFFERENTIAL EQUATIONS”, Differencialʹnye uravneniâ, 60:7 (2024)
Yu. V. Slastushenskiy, D. L. Reviznikov, S. A. Semenov, “Methods for Parametric Identification of Fractional Differential
Equations”, Diff Equat, 60:7 (2024), 941
D. A. Tverdyi, R. I. Parovik, Mathematics of Planet Earth, 12, Hereditary Models of Dynamic Processes in Geospheres, 2024, 177
D. A. Tverdyi, R. I. Parovik, Mathematics of Planet Earth, 12, Hereditary Models of Dynamic Processes in Geospheres, 2024, 193
A. Yu. Morozov, D. L. Reviznikov, “Algorithms for the numerical solution of fractional differential equations with interval parameters”, J. Appl. Industr. Math., 17:4 (2023), 815–827
A.G. Maslovskaya, L.I. Moroz, 2022 Days on Diffraction (DD), 2022, 95
Christina Kuttler, Anna G. Maslovskaya, Lubov I. Moroz, 2021 Days on Diffraction (DD), 2021, 1
Citation in format AMSBIB
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