Numerical Solution of Fractional Benney Equation

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Akınlar M. A., Seçer A., Bayram M.

APPLIED MATHEMATICS & INFORMATION SCIENCES, cilt.8, ss.1633-1637, 2014 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 8
  • Basım Tarihi: 2014
  • Doi Numarası: 10.12785/amis/080418
  • Dergi Adı: APPLIED MATHEMATICS & INFORMATION SCIENCES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1633-1637
  • Anahtar Kelimeler: Fractional Benney equation, Haar wavelets, numerical solution, Caputo fractional derivative
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

In this paper we propose a new solution technique for numerical solution of fractional Benney equation, a fourth degree nonlinear fractional partial differential equation with broad range of applications. The method could be described as a hybrid technique which uses advantages of both wavelets and operational matrices. Having applied the present method, fractional Benney equation is converted into a matrix equation, which is easy to solve. To the best of our knowledge, the fractional Benney equation has not been solved with any numerical or analytical method in the literature. Solving this equation numerically and investigating the applicability of the wavelets on this problem is the main goal of this paper. Haar wavelets and Caputo type fractional derivatives are employed in the calculations. Computational results point the strength of Haar wavelets and feasibility of the present solution algorithm.