Результаты поиска по 'moisture transfer equation':
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  1. Beshtokov M.K.
    Numerical solution of integro-differential equations of fractional moisture transfer with the Bessel operator
    Computer Research and Modeling, 2024, v. 16, no. 2, pp. 353-373

    The paper considers integro-differential equations of fractional order moisture transfer with the Bessel operator. The studied equations contain the Bessel operator, two Gerasimov – Caputo fractional differentiation operators with different orders $\alpha$ and $\beta$. Two types of integro-differential equations are considered: in the first case, the equation contains a non-local source, i.e. the integral of the unknown function over the integration variable $x$, and in the second case, the integral over the time variable τ, denoting the memory effect. Similar problems arise in the study of processes with prehistory. To solve differential problems for different ratios of $\alpha$ and $\beta$, a priori estimates in differential form are obtained, from which the uniqueness and stability of the solution with respect to the right-hand side and initial data follow. For the approximate solution of the problems posed, difference schemes are constructed with the order of approximation $O(h^2+\tau^2)$ for $\alpha=\beta$ and $O(h^2+\tau^{2-\max\{\alpha,\beta\}})$ for $\alpha\neq\beta$. The study of the uniqueness, stability and convergence of the solution is carried out using the method of energy inequalities. A priori estimates for solutions of difference problems are obtained for different ratios of $\alpha$ and $\beta$, from which the uniqueness and stability follow, as well as the convergence of the solution of the difference scheme to the solution of the original differential problem at a rate equal to the order of approximation of the difference scheme.

    Keywords: moisture transfer equation, integro-differential equation, difference schemes, Bessel operator, a priori estimate, stability, convergence.

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