maisМоделирование и анализ информационных системModeling and Analysis of Information Systems1818-10152313-5417Yaroslavl State University10.18255/1818-1015-2016-3-349-356mais-349Research ArticleОригинальные статьиArticlesЧисленное решение одной сингулярно возму- щённой задачи в круговой областиNumerical Solution of a Singularly Perturbed Problem on a Circular DomainХегартиА. Ф.HegartyA. F.

Отделение Математики и Статистики

Department of Mathematics and Statistics

alan.hegarty@ul.ieО’РиорданЮ.O’RiordanE.

Отделение Математических Наук

School of Mathematical Sciences

eugene.oriordan@dcu.ieЛимерикский Университет, ИрландияРоссияUniversity of Limerick, IrelandRussian FederationГородской Университет Дублина, ИрландияРоссияDublin City University, IrelandRussian Federation201620062016233349356Copyright © Хегарти А.Ф., О’Риордан Ю., 20162016Хегарти А.Ф., О’Риордан Ю.Hegarty A.F., O’Riordan E.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.mais-journal.ru/jour/article/view/349

Рассматривается сингулярно возмущенная эллиптическая задача типа конвекция-диффузия в круговой области. С использованием полярных координат, простой схемы с разностями против потока и кусочно-равномерной сетки Шишкина в радиальном направлении для нее строится численный метод, который будет монотонным, поточечно точным и равномерным по параметру при некоторых ограничениях совместности. Приводятся численные эксперименты, иллюстрирующие эффективность данного численного метода в случае, когда эти ограничения ненакладываются на данные задачи.

We consider a singularly perturbed elliptic problem, of convection-diffusion type, posed on a circular domain. Using polar coordinates, simple upwinding and a piecewise-uniform Shishkin mesh in the radial direction, we construct a numerical method that is monotone, pointwise accurate and parameter-uniform under certain compatibility constraints. Numerical results are presented to illustrate the performance of the numerical method when these constraints are not imposed on the data.

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The authors declare that there are no conflicts of interest present.