A Galerkin Finite Element Method to Solve Fractional Diffusion and Fractional Diffusion-Wave Equations

ESEN A., UÇAR Y., Yagmurlu N. M., TASBOZAN O.

MATHEMATICAL MODELLING AND ANALYSIS, cilt.18, sa.2, ss.260-273, 2013 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 18 Sayı: 2
  • Basım Tarihi: 2013
  • Doi Numarası: 10.3846/13926292.2013.783884
  • Dergi Adı: MATHEMATICAL MODELLING AND ANALYSIS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.260-273
  • Anahtar Kelimeler: finite element method, Galerkin method, fractional diffusion equation, fractional diffusion-wave equation, quadratic B-spline
  • İnönü Üniversitesi Adresli: Evet

Özet

In the present study, numerical solutions of the fractional diffusion and fractional diffusion-wave equations where fractional derivatives are considered in the Caputo sense have been obtained by a Galerkin finite element method using quadratic B-spline base functions. For the fractional diffusion equation, the L1 discretizaton formula is applied, whereas the L2 discretizaton formula is applied for the fractional diffusion-wave equation. The error norms L2 and L1 are computed to test the accuracy of the proposed method. It is shown that the present scheme is unconditionally stable by applying a stability analysis to the approximation obtained by the proposed scheme.