The Gegenbauer wavelets-based computational methods for the coupled system of Burgers' equations with time-fractional derivative

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Özdemir N., Seçer A., Bayram M.

Mathematics, cilt.7, 2019 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 7
  • Basım Tarihi: 2019
  • Doi Numarası: 10.3390/math7060486
  • Dergi Adı: Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: Gegenbauer wavelets, coupled Burgers' equations, operational matrix of fractional integration, Galerkin method, collocation method, PARTIAL-DIFFERENTIAL-EQUATIONS, NUMERICAL-SOLUTIONS, COLLOCATION METHOD, SPECTRAL METHODS
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

In this study, Gegenbauer wavelets are used to present two numerical methods for solving the coupled system of Burgers’ equations with a time-fractional derivative. In the presented methods, we combined the operational matrix of fractional integration with the Galerkin method and the collocation method to obtain a numerical solution of the coupled system of Burgers’ equations with a time-fractional derivative. The properties of Gegenbauer wavelets were used to transform this system to a system of nonlinear algebraic equations in the unknown expansion coefficients. The Galerkin method and collocation method were used to find these coefficients. The main aim of this study was to indicate that the Gegenbauer wavelets-based methods is suitable and efficient for the coupled system of Burgers’ equations with time-fractional derivative. The obtained results show the applicability and efficiency of the presented Gegenbaur wavelets-based methods.