Geodesic
Stability and convergence of difference schemes approximating the first boundary value problem for integral-differential parabolic equations in a multidimensional domain
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 3 (2023), pp. 77-91 Cet article a éte moissonné depuis la source Math-Net.Ru

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Integral-differential parabolic equations are studied in a multidimensional domain with boundary conditions of the first kind. For each problem, a difference scheme is constructed with the order of approximation $O(|h|^2+\tau^{m_\sigma})$, where $m_\sigma = 1$ if $\sigma\neq0.5$ and $m_ \sigma = 2$, if $\sigma=0.5$, an a priori estimate is obtained by the method of energy inequalities for solving the difference problem. The obtained estimates imply the uniqueness and stability of the solution with respect to the right-hand side and initial data, as well as the convergence of the solution of the difference problem to the solution of the corresponding original differential problem at a rate of $O(|h|^2+\tau^2)$ for $\sigma = 0.5$.
Keywords: multidimensional problem, first boundary value problem, integral equation, difference scheme, a priori estimate, stability and convergence of difference schemes.
Mots-clés : parabolic equation 
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     title = {Stability and convergence of difference schemes approximating the first boundary value problem for integral-differential parabolic equations in a multidimensional domain},
     journal = {Vestnik Tverskogo gosudarstvennogo universiteta. Seri\^a Prikladna\^a matematika},
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M. KH. Beshtokov; Z. V. Beshtokova. Stability and convergence of difference schemes approximating the first boundary value problem for integral-differential parabolic equations in a multidimensional domain. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 3 (2023), pp. 77-91. http://geodesic.mathdoc.fr/item/VTPMK_2023_3_a4/

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