Concept of modeling uncertainly defined shape of the boundary in two-dimensional boundary value problems and verification of its reliability

Eugeniusz Zieniuk; Marta Kapturczak; Andrzej Kuzelewski

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Concept of modeling uncertainly defined shape of the boundary in two-dimensional boundary value problems and verification of its reliability

机译：二维边界值问题中边界形状不确定定义的建模概念及其可靠性验证

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The paper presents the concept of modeling uncertainly defined shape of the boundary in two-dimensional boundary value problems described by Laplace equation. The authors propose generalization of parametric integral equations system (PIES) in modeling and solving the problems. Previously, PIES was successfully applied to model precisely defined problems. Pseudo-spectral method and modified interval arithmetic are used to define the boundary of the problem and to obtain numerical solution of generalized PIES. We examine direct application of interval Bezier curves in PIES and then we propose our new concept of modeling of the shape of the boundary to improve the reliability of solutions.

机译：本文提出了在由Laplace方程描述的二维边值问题中对边界的不确定定义的形状进行建模的概念。作者提出了参数积分方程系统（PIES）在建模和解决问题中的推广。以前，PIES已成功应用于建模精确定义的问题。伪谱方法和改进的区间算法用于定义问题的边界并获得广义PIES的数值解。我们检查了区间Bezier曲线在PIES中的直接应用，然后提出了边界形状建模的新概念，以提高解的可靠性。

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来源
《Applied Mathematical Modelling》 |2016年第24期|10274-10285|共12页
作者
Eugeniusz Zieniuk; Marta Kapturczak; Andrzej Kuzelewski;
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作者单位

Faculty of Mathematics and Informatics, University of Bialystok, Ciolkowskiego 1 M, Bialystok 15-245, Poland;

Faculty of Mathematics and Informatics, University of Bialystok, Ciolkowskiego 1 M, Bialystok 15-245, Poland;

Faculty of Mathematics and Informatics, University of Bialystok, Ciolkowskiego 1 M, Bialystok 15-245, Poland;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
Uncertainty; Parametric curves; Boundary modeling; PIES; Boundary value problem;

机译：不确定;参数曲线;边界建模;派斯;边值问题;

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Concept of modeling uncertainly defined shape of the boundary in two-dimensional boundary value problems and verification of its reliability

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