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

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Abstract

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.

LanguageEnglish
Pages179-187
Number of pages9
JournalApplied Numerical Mathematics
Volume114
Early online date13 Oct 2016
DOIs
Publication statusPublished - 30 Apr 2017

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Product Integration
Fractional Calculus
Weak Singularity
Fractional Integration
Beta function
Truncation Error
Integrand
Convergence Results
Numerical Examples

Keywords

  • Abel equation
  • discrete fractional calculus
  • numerical integration
  • singular integrand

Cite this

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title = "A novel variant of a product integration method and its relation to discrete fractional calculus",
abstract = "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.",
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