Difference Schemes for the Aller-Lykov Moisture Transfer Equations with a Nonlocal Condition

Lafisheva M. M. , Kerefov M. A. , Dyshekova R. V.
Vladikavkaz Mathematical Journal 2017. Vol. 19. Issue 1.

Abstract:
Questions of warm-moisture transfer in the soil are fundamental in solving of various problems of hydrology, agrophysics, ecology and others. Aller-Lykov equation obtained by introducing additional terms in the moisture transfer equation, which take into account the rapid fluctuations of humidity on the boundaries of the test sample of the soil and the final velocity of the perturbation. The paper deals with a boundary value problem for the Aller-Lykov moisture transfer equation with the first type Steklov conditions. A priori estimate for the solution of the differential problem is obtained by the method of energy inequalities, which implies the stability of its solution. Three-level scheme is built. A priori estimate for the solution of the difference problem is obtained. The fact of the convergence of a difference scheme with a rate of \(O(h+\tau)\) is set. The features of the application of the bordering method to the numerical solution of the difference problem are considered. Numerical experiments are conducted, the results of which are attached.

Keywords: oisture transfer equation, nonlocal conditions, difference scheme, a priori estimate, convergence, bordering method.

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