Abstract
In this paper, we study the third boundary value problem for the convection-diffusion equation with a time fractional derivative and variable coefficients in a multidimensional domain. For an approximate solution in a rectangular parallelepiped of the problem set, in the same area, the third boundary value problem for a differential equation with a small parameter is considered. An a priori estimate is obtained from which it follows the convergence of the solution of the differential problem with a small parameter to the solution of the original problem for small values of the parameter. For a problem with a small parameter, a locally one-dimensional difference scheme by A. A. Samarski is constructed. Using the maximum principle for solving the difference problem, an a priori estimate is obtained in the grid norm \(C\), which expresses the stability of the locally one-dimensional difference scheme. The uniform convergence of the locally one-dimensional scheme is proved for \(0<\alpha<1\).
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Funding
The reported study was funded by RFBR and NSFC according to the research project no. 20-51-53007.
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(Submitted by A. V. Lapin)
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Beshtokov, M.K. A Numerical Method for Solving the Third Boundary Value Problem for the Convection-Diffusion Equation with a Fractional Time Derivative in a Multidimensional Domain. Lobachevskii J Math 42, 1630–1642 (2021). https://doi.org/10.1134/S1995080221070052
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DOI: https://doi.org/10.1134/S1995080221070052