Numerical Caputo Differentiation by Radial Basis Functions

Ming Li*, Yujiao Wang, Leevan LING

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

Previously, based on the method of (radial powers) radial basis functions, we proposed a procedure for approximating derivative values from one-dimensional scattered noisy data. In this work, we show that the same approach also allows us to approximate the values of (Caputo) fractional derivatives (for orders between 0 and 1). With either an a priori or a posteriori strategy of choosing the regularization parameter, our convergence analysis shows that the approximated fractional derivative values converge at the same rate as in the case of integer order 1.

Original languageEnglish
Pages (from-to)300-315
Number of pages16
JournalJournal of Scientific Computing
Volume62
Issue number1
DOIs
Publication statusPublished - 1 Jan 2015

Scopus Subject Areas

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Engineering(all)
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Convergence analysis
  • Fractional derivatives
  • Inverse problem
  • Noisy data
  • Regularization

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