A novel variant of a product integration method and its relation to discrete fractional calculus

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• 作者：S. McKee^a ; ^{s.mckee@strath.ac.uk} ; Jose A. Cuminato^b ; ^{jacuminato@gmail.com}
• 关键词：Numerical integration ; Singular integrand ; Abel equation ; Discrete fractional calculus
• 刊名：Applied Numerical Mathematics
• 出版年：2017
• 出版时间：April 2017
• 年：2017
• 卷：114
• 期：Complete
• 页码：179-187
• 全文大小：234 K
• 卷排序：114

文摘

A new integration technique, which is suitable for integrands with multiple weak singularities, is introduced. Local truncation errors are given. This scheme, when applied to the Beta function, is shown to emerge naturally from discrete fractional integration. To illustrate the effectiveness of the integration method a numerical example is provided, with somewhat unexpected convergence results.