ON THE STABILITY OF THE GALERKIN METHOD FOR SOLVING THE PROBLEM OF DETERMINING THE WARM-MOISTURE STATE OF RAW COTTON

Authors

  • A.Z.Mamatov Professor of the Tashkent Institute of Textile and Light Industry, Tashkent city, Uzbekistan
  • J.T. Raxmanov Basic doctorant of Gulistan State University, Syrdarya region, town of Gulistan, Uzbekistan
  • N.O.Sulaymanova Intern teacher of Guliston State Pedagogical Institute

Keywords:

mathematical model, algorithm, temperature, coordinate system, monotonicity, stability, strong minimality,.

Abstract

The article considers a boundary value problem for systems consisting of two differential equations of parabolic type to determine the heat-moist state of raw cotton in a direct-flow drum dryer. An approximate solution of the Galerkin method for the problem under consideration is constructed. The stability of the Galerkin method for the approximate solution of the problem under consideration is established under the condition of strongly minimal coordinate systems.

References

Mamatov A., Parpiev A., Shorakhmedova, M. Mathematical model for calculating the temperature field of a direct-flow drying drum. Journal of Physics: Conference Seriesthis link is disabled, 2021, 2131(5), 052067

Mamatov, A., Bakhramov S., Narmamatov A. An approximate solution by the Galerkin method of a quasilinear equation with a boundary condition containing the time derivative of the unknown function. AIP Conference Proceedingsthis link is disabled, 2021, 2365, 070003

Mamatov A.Z., Usmankulov A.K., Abbazov I.Z., Norboyev U.A., Mukhametshina E.T. Determination of Temperature of Components of Cotton-Raw Material in a Drum Dryer with a Constant. IOP Conference Series: Earth and Environmental Sciencethis link is disabled, 2021, 939(1), 012052

Mamatov A.Z., Pardaev X.N., Mardonov, J.S.H., Plekhanov, A.F. Determining of the heat-moisture stateof raw cotton in a drum dryer. Izvestiya Vysshikh Uchebnykh Zavedenii, Seriya Teknologiya Tekstil'noi Promyshlennostithis link is disabled, 2021, 391(1), С. 46–49

Mamatov A., Parpiyev A., Kayumov A., Мathematical models of the heat and mass exchange process during pneumo-transportation of cotton-raw// International Scientific Journal Theoretical & Applied Science , p-ISSN: 2308-4944 (print) e-ISSN: 2409-0085 (online) , Year: 2020 Issue: 11 ,Volume: 91 Р.508-513.

Mamatov A.Z., Axmatov N. Chislennoe reshenie zadachi opredeleniya teplo-vlazhnogo sostoyaniya xlopka-syrtsa v barabannoy sushilke // J.Toʻqimachilik muammolari.-2016.-№3,-B.80-86.

Mamatov A.Z., Djumabaev G. Ob ustoychivosti priblijennogo resheniya odnoy zadache opredeleniya teplo-vlazhnogo sostoyaniya xlopka-syrtsa //

J. Problemy tekstilya. 2010.-№2, P. 86-90

Mixlin S.G. Chislennaya realizatsiya variatsionnyx metodov. M.-Nauka,-1966.-432 Pages.

Mamatov A.Z. Primeneniya metoda Galerkina k nekotoromu kvazilineynomu uravneniyu parabolicheskogo tipa // Vestnik LGU,-1981.-№13.-P.37-45.

Mamatov A.Z., Baxramov S. Priblizhennoe reshenie metoda Galerkina kvazilineynogo uravneniya s granichno’m usloviem, soderjahiy proizvodnuyu po vremeni ot iskomoy funktsi // Uzbekistan -Malaysia inter. scientific online conference, Uz.NU, 24-25 august 2020 y., 239 p.

Mamatov A.Z., Dosanov M.S., Raxmanov J., Turdibaev D.X. Odna zadacha parabolicheskogo tipa s divergentnoy glavnoy chastyu // NAU (Natsionalnaya assotsiatsiya uchenyx). Monthly scientific journal, 2020, №57, 1-part, P.59-63.

Mamatov, A.Z., Narjigitov Х., Kengash J ., Rakhmanov J., Stability of the Galerkin Method for one Quasilinear Parabolic Type Problem// CENTRAL ASIAN JOURNAL OF MATHEMATICAL THEORY AND COMPUTER SCIENCES 2 (6), 6-12, 2021

Mamatov, A.Z., Narjigitov Х., Rakhmanov J., Turdibayev D. Refining the Galerkin method error estimation for parabolic type problem with a boundary condition E3S Web of Conferences 304, 03019 (2021) ICECAE 2021 https://doi.org/10.1051/e3sconf/202130403019

Ladyzhenskaya O.A., Solonnikov V.A., Uraltseva N.N. Lineyniye i kvazilineyniye uravneniya parabolicheskogo tipa. M.-Nauka,-1967.-736 P.

Ladyzhenskaya О. A., Uraltseva N.N. Lineyniye i kvazilineynie uravneniya ellipticheskogo tipa. М.-Наука,-1973.-576 С.

Wheeler M.F. A priori error estimates for Galerkin approximation to parabolic partial differential equations. SIAM J. Numer. Anal.1973.-10.-P.723-759.

Downloads

Published

2023-06-13

How to Cite

Mamatov , A., Raxmanov , J., & Sulaymanova, N. (2023). ON THE STABILITY OF THE GALERKIN METHOD FOR SOLVING THE PROBLEM OF DETERMINING THE WARM-MOISTURE STATE OF RAW COTTON. International Bulletin of Engineering and Technology, 3(6), 101–107. Retrieved from https://internationalbulletins.com/intjour/index.php/ibet/article/view/788