COMPACT DIFFERENCE SCHEMES FOR THE ALLER-LYKOV MOISTURE TRANSFER EQUATION (DIGITAL TRANSFORMATION AND ARTIFICIAL INTELLIGENCE, 2025)
The generalized Aller-Lykov equation is a mathematical model for many applied heat and moisture transfer problems. This includes nonstationary problems in hydrogeology, agrophysics, biology, ecology, and other fields, which are primarily solved using numerical methods. In this paper, high-precision difference schemes (compact schemes) are constructed and analyzed for the nonstationary generalized Aller-Lykov equation. The scheme is constructed in space and time using the finite difference method. The stability and convergence of the resulting difference scheme are proven, and accuracy estimates are obtained for a sufficiently smooth solution to the original differential problem. An implementation algorithm for the constructed scheme is proposed.