Modified spline collocation for linear fractional differential equations

Marek Kolk ^[1] ; Arvet Pedas ^[1] ; Enn Tamme ^[1]
1. [1] University of Tartu
  
  University of Tartu
  
  Tartu linn, Estonia
Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 283, Nº 1 (1 August 2015), 2015, págs. 28-40
Idioma: inglés
DOI: 10.1016/j.cam.2015.01.021
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Resumen
- We propose and analyze a class of high order methods for the numerical solution of initial value problems for linear multi-term fractional differential equations involving Caputo-type fractional derivatives. Using an integral equation reformulation of the initial value problem we first regularize the solution by a suitable smoothing transformation. After that we solve the transformed equation by a piecewise polynomial collocation method on a mildly graded or uniform grid. Optimal global convergence estimates are derived and a superconvergence result for a special choice of collocation parameters is established. Theoretical results are verified by some numerical examples.