The method of mechanical quadratures for integral equations with fixed singularity

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• 作者：L. A. Onegov
• 刊名：Russian Mathematics (Iz VUZ)
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：60
• 期：7
• 页码：71-78
• 全文大小：559 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Russian Library of Science
  
• 出版者：Allerton Press, Inc. distributed exclusively by Springer Science+Business Media LLC
• ISSN：1934-810X
• 卷排序：60

文摘

We investigate the method of mechanical quadratures for integral equations with fixed singularity. We establish estimates of the error of this method based on a quadrature process, which is the best in the class of differentiable functions. We prove the convergence of the method in finite-dimensional and uniform metrics. We find that the investigated quadrature method is optimal by order on the Hölder class of functions.Keywordsintegral equationquadrature processsolutionconvergenceaccuracyoptimality