Abstract
The paper presents a new mathematical model of the convection-diffusion process with ‘memory along the flow path’. It is described by one-dimensional initial-boundary value problem with a fractional derivative along the characteristic curve of convection operator. The proposed model satisfies local and global conservation laws. A finite difference approximation of the problem is constructed based on the Lagrange approach. Stability and discrete conservation law are proved for the algorithmic implementation of this approximation. A numerical example demonstrates the properties of the constructed algorithm.
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This work was supported by Russian Scientific Foundation, project no. 20-61-46017.
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(Submitted by A. M. Elizarov)
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Shaydurov, V., Petrakova, V. & Lapin, A. A Fokker–Planck Equation with a Fractional Derivative Along the Trajectory of Motion with Conservation Law. Lobachevskii J Math 43, 1043–1055 (2022). https://doi.org/10.1134/S1995080222070216
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DOI: https://doi.org/10.1134/S1995080222070216