Compact difference schemes for moisture transfer equations

The construction of stable and economical numerical algorithms of high accuracy is a relevant issue in the modern theory of numerical methods. Such algorithms appear when solving initial boundary value problems for linear and nonlinear nonstationary equations. In this article, results are obtained on the construction and study of difference schemes of high accuracy (compact difference schemes) based on finite difference and finite element methods for the nonstationary generalized Aller-Lykov equation. By developing the apparatus of the theory of stability of difference schemes, a priori estimates for the error in the class of smooth solutions of the original differential problem are obtained. By using this estimate, it is possible to prove the convergence of the constructed algorithm with a fourth-order velocity in time and space variables. An algorithm for implementing the constructed scheme is proposed.