Numerical solution for a class of fractional convection-diffusion equations using the flatlet oblique multiwavelets

Irandoust-Pakchin S., Dehghan M., Abdi-Mazraeh S., Lakestanı M.

JVC/Journal of Vibration and Control, cilt.20, sa.6, ss.913-924, 2014 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 20 Sayı: 6
  • Basım Tarihi: 2014
  • Doi Numarası: 10.1177/1077546312470473
  • Dergi Adı: JVC/Journal of Vibration and Control
  • Derginin Tarandığı İndeksler: Scopus
  • Sayfa Sayıları: ss.913-924
  • Anahtar Kelimeler: biorthogonal system, Caputo derivative, flatlet oblique multiwavelets, Fractional-order differential equations, operational matrix
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

This paper is concerned with the construction of biorthogonal multiwavelet basis in the unit interval to form a biorthogonal flatlet multiwavelet system. Next a method to calculate integer and fractional derivatives of the dual flatlet multiwavelets by multiplying some matrices is suggested. The system is then used to solve a fractional convection-diffusion equation. The biorthogonality and high vanishing moments properties of this system result in efficient and accurate solutions. Finally, numerical results for some test problems with known solutions are presented and the absolute errors are compared with the errors resulting from the other bases. © The Author(s) 2013 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav.