A performance assessment of an HDG method for second-order Fredholm integro-differential equation: existence-uniqueness and approximation

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Karaaslan M. F.

TURKISH JOURNAL OF MATHEMATICS, cilt.45, ss.2269-2281, 2021 (SCI-Expanded) identifier identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 45
  • Basım Tarihi: 2021
  • Doi Numarası: 10.3906/mat-2102-18
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.2269-2281
  • Anahtar Kelimeler: Hybridization, Fredholm integro-differential equation, stabilization parameter, boundary value problem, COLLOCATION METHOD, DISCONTINUOUS GALERKIN, NONLINEAR FREDHOLM
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

In this paper, we obtain the existence-uniqueness of solution to the second-order linear Fredholm integrodifferential equation (FIDE) with Dirichlet boundary condition by hybridizable discontinuous Galerkin (HDG) method. A key property of these methods is to eliminate all internal degrees of freedom and to construct a linear system that only includes globally coupled unknowns at the element interfaces. After designing and implementing HDG algorithm, we provide some necessary and sufficient conditions based on the stabilization parameter and kernel function to guarantee the existence-uniqueness of the approximate solution. Then, some numerical examples are carried out to assess the performance of the present method. When comparing with existing some methods in literature, the experimental studies verify the reliability and feasibility of the HDG method for the problem under consideration.