A diffusion–convection problem with a fractional derivative along the trajectory of motion
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Alexander V. Lapin
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Vladimir V. Shaidurov
Abstract
A new mathematical model of the diffusion–convective process with ‘memory along the flow path’ is proposed. This process is described by a homogeneous one-dimensional Dirichlet initial-boundary value problem with a fractional derivative along the characteristic curve of the convection operator. A finite-difference approximation of the problem is constructed and investigated. The stability estimates for finite-difference schemes are proved. The accuracy estimates are given for the case of sufficiently smooth input data and the solution.
Funding statement: This work was supported by the Russian Science Foundation, project No. 20-61-46017.
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© 2021 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Maximum cross section method in the filtering problem for continuous systems with Markovian switching
- High precision methods for solving a system of cold plasma equations taking into account electron–ion collisions
- A diffusion–convection problem with a fractional derivative along the trajectory of motion
- An implicit scheme for simulation of free surface non-Newtonian fluid flows on dynamically adapted grids
- Model reduction for Smoluchowski equations with particle transfer
Artikel in diesem Heft
- Frontmatter
- Maximum cross section method in the filtering problem for continuous systems with Markovian switching
- High precision methods for solving a system of cold plasma equations taking into account electron–ion collisions
- A diffusion–convection problem with a fractional derivative along the trajectory of motion
- An implicit scheme for simulation of free surface non-Newtonian fluid flows on dynamically adapted grids
- Model reduction for Smoluchowski equations with particle transfer
