COMPACT DIFFERENCE SCHEMES FOR THE ALLER-LYKOV MOISTURE TRANSFER EQUATION

Tleuov Kuatbay Orazbayevich

Authors

Tleuov Kuatbay Orazbayevich Tashkent State Technical University named after Islam Karimov

Abstract

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.

References

10. Utebaev D., Utepbergenova G.X., Tileuov K.O. On Convergence of Schemes of Finite Element Method of High Accuracy for the Equation of Heat and Moisture Transfer // Bulletin of the Karaganda University. Series Mathematics, 2021, № 2(102), C. 129-141. http://mathematics-vestnik.ksu.kz

11. Utebaev D., Utepbergenova G., Tileuov K. Comparison of Some Numerical Methods for Solving Boundary-Volue Problems for a Generalized Equation of Moisture Transfer // Materials AIP Conference Proceedings, 2022, Vol. 2636, Pp. 040009-1-6. https://aip.scitation.org/doi/10.1063/5.0104436.

12. Utebaev D., Utepbergenova G., Tileuov K. On Convergence of Difference Schemes for the Generalized Equation of Moisture Transfer in a Weak Metric // Bulletin of the Institute of Mathematics, 2021, № 4(6), Pp. 31-41.

13. 13. Moskalkov M.N., Utebaev D. Convergence of the Finite Element Scheme for the Equation of Internal Waves // Cybernetics and Systems Analysis, 2011, Vol. 47, No. 3, Pp. 459 – 465.

14. Moskalkov M.N., Utebaev D. Comparison of Some Methods for Solving the Internal Wave Propagation Problem in a Weakly Stratified Fluid // Mathematical models and Computer Simulations, 2011, Vol. 3, No. 2, Pp. 264–271: DOI:10.1134/S2070048211020086.

15. Aripov M., Utebaev D., Nurullaev Zh. Convergence of high-precision finite element method schemes for the two-temperature plasma equation // Materials AIP Conference Proceedings, 09 February 2021, Vol. 2325, Pp. 020059-1-6. https://aip.scitation.org/journal/apc, https://doi.org/10.1063/12.0003133

16. Utebaev D., Utebaev B. Comparison of Some Numerical Methods Solutions of Wave Equations With Strong Dispersion // International Uzbekistan-Malaysia Conference on «Computational Models and Technologies» (CMT 2020), Materials AIP Conference Proceedings, 2021, Vol. 2365, Pp. 020009-1-9. https://proceedings.aip, https://doi.org/10.1063/5.0058159

18. Aripov M.M., Utebaev D., Nurullaev Zh.A. On the convergence of difference schemes of high accuracy for the equation of ion-acoustic waves in a magnetized plasma // Bulletin of the Karaganda University. Series Mathematics, 2022, № 4 (108), pp. 4-19. https://mathematics-vestnik.ksu.kz/apart/2022-108-4/1.pdf.