A hybridizable discontinuous Galerkin method for a class of fractional boundary value problems

KARAASLAN M. F., Celiker F., KURULAY M.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, cilt.333, ss.20-27, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 333
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1016/j.cam.2017.09.043
  • Dergi Adı: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.20-27
  • Anahtar Kelimeler: Hybridizable discontinuous Galerkin methods, Fractional boundary value problems, Caputo derivative, DIFFERENTIAL-EQUATIONS
  • Marmara Üniversitesi Adresli: Hayır

Özet

In this paper, we present a hybridizable discontinuous Galerkin (HDG) method for solving a class of fractional boundary value problems involving Caputo derivatives. The HDG methods have the computational advantage of eliminating all internal degrees of freedom and the only globally coupled unknowns are those at the element interfaces. Furthermore, the global stiffness matrix is tridiagonal, symmetric, and positive definite. Internal degrees of freedom are recovered at an element-by-element postprocessing step. We carry out a series of numerical experiments to ascertain the performance of the proposed method. (C) 2017 Elsevier B.V. All rights reserved.