A B-spline collocation method for solving fractional diffusion and fractional diffusion-wave equations

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

TBILISI MATHEMATICAL JOURNAL, cilt.8, sa.2, ss.181-193, 2015 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 8 Sayı: 2
  • Basım Tarihi: 2015
  • Doi Numarası: 10.1515/tmj-2015-0020
  • Dergi Adı: TBILISI MATHEMATICAL JOURNAL
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI)
  • Sayfa Sayıları: ss.181-193
  • Anahtar Kelimeler: Finite element method, Collocation method, Fractional diffusion equation, Fractional diffusion-wave equation, Cubic B-spline
  • İnönü Üniversitesi Adresli: Evet

Özet

In this paper,we have considered the fractional diffusion and fractional diffusion wave equations in which the time derivative is a fractional derivative in the Caputo form and have obtained their numerical solutions by collocation method using cubic B-spline base functions. In the solution process, for the fractional diffusion equation L1 discretizaton formula of the fractional derivative is applied, and for the fractional diffusion-wave equation L2 discretizaton formula of the fractional derivative is applied. Accuracy of the proposed method is discussed by computing the error norms L2 and L-infinity. A stability analysis of the approximation obtained by the scheme shows that the method is unconditionally stable.