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Central part interpolation schemes for a class of fractional initial value problems

Authors

  • Mikk Vikerpuur University of Tartu
  • Margus Lillemäe University of Tartu
  • Arvet Pedas University of Tartu

DOI:

https://doi.org/10.12697/ACUTM.2022.26.11

Keywords:

Fractional integro-differential equation, Caputo fractional derivative, weakly singular integral equation, central part interpolation, collocation method

Abstract

We consider an initial value problem for linear fractional integro-differential equations with weakly singular kernels. Using an integral equation reformulation of the underlying problem, a collocation method based on the central part interpolation by continuous piecewise polynomials on the uniform grid is constructed and analysed. Optimal convergence order of the proposed method is established and confirmed by numerical experiments.

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Author Biographies

Mikk Vikerpuur, University of Tartu

Institute of Mathematics and Statistics

Margus Lillemäe, University of Tartu

Institute of Mathematics and Statistics

Arvet Pedas, University of Tartu

Institute of Mathematics and Statistics

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Published

2022-05-27

Versions

Issue

Vol. 26 No. 1 (2022)

Section

Articles