Boundary value problems for a loaded modified fractional-order moisture transfer equation with the Bessel operator and difference methods for their solution

M. Kh. Beshtokov

Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 30 (2020) no. 2, pp. 158-175

Résumé

The paper is devoted to the construction of approximate solutions of boundary value problems in a rectangle for a loaded modified fractional-order moisture transfer equation with the Bessel operator, which act as mathematical models of the movement of moisture and salts in soils with fractal organization. Difference schemes for differential problems are constructed. The method of energy inequalities is used to derive a priori estimates of solutions to the problems under consideration in differential and difference interpretations. The obtained a priori estimates are followed by uniqueness, stability of the solution from the initial data and the right part, as well as convergence of the solution of the difference problem to the solution of the corresponding differential problem with a speed equal to the order of approximation error. An algorithm for the numerical solution of difference schemes obtained by approximating boundary value problems for a loaded modified fractional-order moisture transfer equation with the Bessel operator is constructed.

Détail

Keywords: boundary value problems, loaded equations, difference scheme, moisture transfer equation, Caputo fractional derivative.
Mots-clés : a priori estimation, pseudoparabolic equation, Hallaire's equation

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