High-order Legendre collocation method for fractional-order linear semi-explicit differential algebraic equations. ETNA - Electronic Transactions on Numerical Analysis
Fiche du document
15 novembre 2018
- handle: 10670/1.mx5py1
- issn: 1068-9613
- doi: 10.1553/etna_vol48s387
info:eu-repo/semantics/openAccess
Sujets proches
Examples Exemplars Science and space Space research Parliamentary government Representation Self-government Political representation Natural philosophy Philosophy, Natural Papers Exploration of space Space research Solar system--Exploration Space exploration (Astronautics)Citer ce document
F. Ghanbari et al., « High-order Legendre collocation method for fractional-order linear semi-explicit differential algebraic equations. ETNA - Electronic Transactions on Numerical Analysis », Elektronisches Publikationsportal der Österreichischen Akademie der Wissenschafte, ID : 10.1553/etna_vol48s387
Métriques
Partage / Export
Résumé
This paper is devoted to a high-order Legendre collocation approximation for solving fractional-order linear semi-explicit differential algebraic equations numerically. We discuss existence, uniqueness, and regularity results and conclude that the solutions typically suffer from a singularity at the origin. Moreover, we show that the representation of the approximate solutions by a linear combination of Legendre polynomials leads to unsatisfactory convergence results. To overcome this difficulty, we develop a new regularization approach that removes the singularity of the input data and produces approximate solutions of higher accuracy. Illustrative numerical examples are presented to support the obtained theoretical results.