Разработка разностных схем для сингулярно-возмущенных задач.
Исследование двухсеточного метода.
Метод Ричардсона
Основные публикации:
S. V. Tikhovskaya, “A Cascadic Multigrid Algorithm on the Shishkin Mesh for a Singularly Perturbed Elliptic Problem with regular layers”, XV International Scientific and Technical Conference “Applied Mechanics and Systems Dynamics” AMSD 2021 (Omsk, Russian Federation, 09.11 – 11.11.2021), Journal of Physics: Conference Series, 2182, 2022, 012034 , 9 pp.
S. V. Tikhovskaya, “A cascadic multigrid algorithm on the Shishkin mesh for a singularly perturbed elliptic problem”, V International Scientific and Technical Conference “Mechanical Science and Technology Update” MSTU-2021 (Omsk, Russian Federation, 16.03 – 17.03.2021), Journal of Physics: Conference Series, 1901, 2021, 012052 , 8 pp.
S. V. Tikhovskaya, M. F. Korbut, “Two-grid algorithm for a system of singularly perturbed reaction-diffusion equations on Shishkin mesh”, IV International Scientific and Technical Conference “Mechanical Science and Technology Update” (MSTU-2020) (Omsk, Russian Federation, 17.03 – 19.03.2020), Journal of Physics: Conference Series, 1546, 2020, 012104 , 8 pp.
S. V. Tikhovskaya, M. F. Korbut, “Two-grid algorithm for the solution of singularly perturbed two-parameter problem on Shishkin mesh”, 12th International Scientific and Technical Conference on Applied Mechanics and Systems Dynamics (AMSD 2018) (Omsk, Russian Federation, 13.11 – 15.11.2018), Journal of Physics: Conference Series, 1210, 2019, 012142 , 8 pp.
A. I. Zadorin, S. V. Tikhovskaya, “Formulas of numerical differentiation on a uniform mesh for functions with the exponential boundary layer”, International Journal of Numerical Analysis and Modeling, 16:4 (2019), 590–608www.math.ualberta.ca/ijnam/Volume-16-2019/No-4-19/2019-04-04.pdf
S. V. Tikhovskaya, “Solving a Singularly Perturbed Elliptic Problem by a Cascadic Multigrid Algorithm with Richardson Extrapolation”, Finite Difference Methods. Theory and Applications. FDM 2018. (Lozenetz, Bulgaria, 11.06 – 16.06.2018), Lecture Notes in Computer Science, 11386, 2019, 533–541
S. V. Tikhovskaya, “Analysis of the numerical differentiation formulas of functions with large gradients”, Ninth International Conference on Application of Mathematics in Technical and Natural Sciences (AMiTaNS-2017) (Albena, Bulgaria, 21.06 – 26.06.2017), AIP Conference Proceedings, 1895, 2017, 110010 , 9 pp.
S. V. Tikhovskaya, “Solving a singularly perturbed elliptic problem by a multigrid algorithm with Richardson extrapolation”, Sixth Conference on Numerical Analysis and Its Applications (NAA'2016) (Lozenetz, Bulgaria, 15.06 – 22.06.2016), Lecture Notes in Computer Science, 10187, 2017, 674–681
S. V. Tikhovskaya, A. I. Zadorin, “Analysis of polynomial interpolation of the function of two variables with large gradients in the parabolic boundary layers”, Eighth International Conference on Application of Mathematics in Technical and Natural Sciences (AMiTaNS-2016) (Albena, Bulgaria, 22.06 – 27.06.2016), AIP Conference Proceedings, 1773, 2016, 100008 , 9 pp.
S. V. Tikhovskaya , A. I. Zadorin, “A Two-grid Method with Richardson Extrapolation For a Semilinear Convection-diffusion Problem”, Seventh International Conference on Application of Mathematics in Technical and Natural Sciences (AMiTaNS-2015) (Albena, Bulgaria, 28.06 – 03.07.2015), AIP Conference Proceedings, 1684, 2015, 090007 , 8 pp.
С. В. Тиховская, “Исследование двухсеточного метода повышенной точности для эллиптического уравнения реакции–диффузии с пограничными слоями”, Учëн. зап. Казан. гос. ун-та. Сер. Физ.-матем. науки, 157:1 (2015), 60–74
A. I. Zadorin, S. V. Tikhovskaya, N. A. Zadorin, “A two-grid method for elliptic problem with boundary layers”, Applied Numerical Mathematics, 93 (2015), 270–278
С. В. Тиховская, Разработка разностных схем на сгущающихся сетках для краевых задач с пограничным слоем, диссертация ... кандидата физико-математических наук, Омский филиал Института математики им. С.Л. Соболева, Омск, 2013 , 105 с. "www.sscc.ru/Diss_sov/Tikhovskaya.pdf
А. И. Задорин, С. В. Тиховская, “Двухсеточный метод для нелинейной сингулярно возмущенной краевой задачи на сетке Шишкина”, Сиб. журн. индустр. матем., 16:1 (2013), 42–55 , RSCI:18966109
А. И. Задорин, С. В. Тиховская, “Решение нелинейного сингулярно возмущенного уравнения второго порядка на основе схемы Самарского”, Сиб. журн. вычисл. матем., 16:1 (2013), 11–25 , RSCI:18928643 ; A. I. Zadorin, S. V. Tikhovskaya, “Solving a second-order nonlinear singular perturbation ordinary differential equation by a Samarskii scheme”, Num. Anal. Appl., 6:1 (2013), 9–23 , WOS:000219643200002
С. В. Тиховская, “Двухсеточный метод для эллиптического уравнения с пограничными слоями на сетке Шишкина”, Учён. зап. Казан. гос. ун-та. Сер. Физ.-матем. науки, 154:4 (2012), 49–56; S. V. Tikhovskaya, “A Two-Grid Method for an Elliptic Equation with Boundary Layers on a Shishkin Mesh”, Lobachevskii Journal of Mathematics, 35:4 (2014), 409–415 , WOS:000213043900019
А. И. Задорин, С. В. Тиховская, “Разностная схема на равномерной сетке для сингулярно возмущенной задачи Коши”, Вестн. НГУ. Сер. матем., мех., информ., 11:3 (2011), 114–122 , RSCI:16990940 ; A. I. Zadorin, S. V. Tikhovskaya, “Difference scheme on a uniform grid for the singularly perturbed Cauchy problem”, Journal of Mathematical Sciences, 195:6 (2013), 865–872
А. И. Задорин, С. В. Тиховская, “Анализ разностной схемы для сингулярно возмущенной задачи Коши на сгущающейся сетке”, Сиб. журн. вычисл. матем., 14:1 (2011), 47–57; A. I. Zadorin, S. V. Tikhovskaya, “Analysis of a difference scheme for a singular perturbation Cauchy problem on refined grids”, Num. Anal. Appl., 4:1 (2011), 36–45 , WOS:000219603500004
