Информация о публикации

Просмотр записей

Инд. авторы:	Blokhin A.M., Kruglova E.A., Semisalov B.V.
Заглавие:	Estimation of two error components in the numerical solution to the problem of nonisothermal flow of polymer fluid between two coaxial cylinders
Библ. ссылка:	Blokhin A.M., Kruglova E.A., Semisalov B.V. Estimation of two error components in the numerical solution to the problem of nonisothermal flow of polymer fluid between two coaxial cylinders // Computational Mathematics and Mathematical Physics. - 2018. - Vol.58. - Iss. 7. - P.1099-1115. - ISSN 0965-5425. - EISSN 1555-6662.
Внешние системы:	DOI: 10.1134/S0965542518070035; РИНЦ: 35761384; SCOPUS: 2-s2.0-85052233303; WoS: 000442613300009;
Реферат:	eng: Abstract: An algorithm for solving a stationary nonlinear problem of a nonisothermal flow of an incompressible viscoelastic polymer fluid between two coaxial cylinders is developed on the basis of Chebyshev approximations and the collocation method. In test calculations, the absence of saturation of the algorithm is shown. A posteriori estimates of two error components in the numerical solution—the error of approximation method and the round-off error—are obtained. The behavior of these components as a function of the number of nodes in the spatial grid of the algorithm and the radius of the inner cylinder is analyzed. The calculations show exponential convergence, stability to rounding errors, and high time efficiency of the algorithm developed.
Ключевые слова:	error estimates; collocation method; polymer fluid dynamics; algorithm without saturation; Chebyshev polynomials; exponential convergence;
Издано:	2018
Физ. характеристика:	с.1099-1115
Цитирование:	1. H. Qin, Yi, Cal, J. Dong, and Y.-S. Lee, “Direct printing of capacitive touch sensors on flexible substrates by additive e-jet printing with silver nanoinks,” J. Manufact. Sci. Eng. 139 (031011), 1–7 (2017) 2. V. I. Tuev, N. D. Malyutin, A. G. Loshchilov, et al., “Application of the additive printer (plotter) technology in electronics to form films from organic and inorganic materials,” Dokl. Tomsk. Univ. Sist. Upr. Radioelekyton., No. 4, 52–63 (2015) 3. V. N. Pokrovskii, The Mesoscopic Theory of Polymer Dynamics, 2nd ed. (Springer, Berlin, 2010) 4. Yu. A. Altukhov, A. S. Gusev, and G. V. Pyshnograi, Introduction to the Mesoscopic Theory of Fluid Polymer Systems (AltGPA, Barnaul, 2012) [in Russian] 5. A. M. Blokhin and A. S. Rudometova, “Stationary solutions of the equations for nonisothermal electroconvection of a weakly conducting incompressible polymeric liquid,” J. Appl. Ind. Math. 9 (2), 147–156 (2015) 6. A. M. Blokhin, A. V. Yegitov, and D. L. Tkachev, “Linear instability of solutions in a mathematical model describing polymer flows in an infinite channel,” Comput. Math. Math. Phys. 55 (5), 848–873 (2015) 7. A. M. Blokhin, E. A. Kruglova, and B. V. Semisalov, “Steady-state flow of an incompressible viscoelastic polymer fluid between two coaxial cylinders,” Comput. Math. Math. Phys. 57 (7), 1181–1193 (2017) 8. A. M. Blokhin, B. V. Semisalov, and A. S. Shevchenko, “Stationary solutions of equations describing the nonisothermal flow of an incompressible viscoelastic polymeric fluid,” Mat. Model. 28 (10), 3–22 (2016) 9. A. M. Blokhin and B. V. Semisalov, “A stationary flow of an incompressible viscoelastic fluid in a channel with elliptic cross section,” J. Appl. Ind. Math. 9 (1), 18–26 (2015) 10. K. I. Babenko, Fundamentals of Numerical Analysis (Fizmatlit, Moscow, 1986) [in Russian] 11. B. V. Semisalov, “A fast nonlocal algorithm for solving Neumann–Dirichlet boundary value problems with error control,” Vychisl. Metody Program. 17 (4), 500–522 (2016) 12. V. K. Dzyadyk, Introduction to the Theory of Uniform Approximation of Functions by Polynomials (Nauka, Moscow, 1977) [in Russian] 13. N. S. Bakhvalov, N. P. Zhidkov, and G. M. Kobel’kov, Numerical Methods, 6th ed. (BINOM, Moscow, 2008) [in Russian] 14. L. N. Trefethen, Approximation Theory and Approximation Practice (SIAM, Philadelphia, 2013) 15. S. M. Rump, “Verification methods: Rigorous results using floating-point arithmetic,” Acta Numerica 19, 287–449 (2010) 16. G. Alefeld and J. Herzberger, Introduction to Interval Computations (Academic, New York, 1983) 17. S. K. Godunov, A. G. Antonov, O. P. Kiriljuk, and V. I. Kostin, Guaranteed Accuracy in Numerical Linear Algebra (Springer, Netherlands, 1993) 18. E. A. Biberdorf and N. I. Popova, Guaranteed Accuracy of Modern Linear Algebra Algorithms (Sib. Otd. Ross. Akad. Nauk, Novosibirsk, 2006) [in Russian] 19. J. W. Demmel, Applied Numerical Linear Algebra (SIAM, Philadelphia, PA, 1997) 20. V. A. Trenogin, Functional Analysis (Nauka, Moscow, 1980) [in Russian] 21. A. Yu. Gornov, Computational Techniques for Solving Optimal Control Problems (Nauka, Novosibirsk, 2009) [in Russian]