A JACOBI WAVELET COLLOCATION METHOD FOR FRACTIONAL FISHER'S EQUATION IN TIME


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Seçer A. , Cinar M.

THERMAL SCIENCE, vol.24, 2020 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 24
  • Publication Date: 2020
  • Doi Number: 10.2298/tsci20s1119s
  • Title of Journal : THERMAL SCIENCE
  • Keywords: time-fractional Fisher's equation, collocation method, fractional differential equation, Jacobi wavelet, HOMOTOPY-PERTURBATION METHOD, OPERATIONAL MATRICES

Abstract

In this study, the Jacobi wavelet collocation method is studied to derive a solution of the time-fractional Fisher's equation in Caputo sense. Jacobi wavelets can be considered as a generalization of the wavelets since the Gegenbauer, and thus also Chebyshev and Legendre polynomials are a special type of the Jacobi polynomials. So, more accurate and fast convergence solutions can be possible for some kind of problems thanks to Jacobi wavelets. After applying the proposed method to the considered equation and discretizing the equation at the collocation points, an algebraic equation system is derived and solving the equation system is quite simple rather than solving a non-linear PDE. The obtained values of our method are checked against the other numerical and analytic solution of considered equation in the literature and the results are visualized by using graphics and tables so as to reveal whether the method is effectiveness or not. The obtained results evince that the wavelet method is quite proper because of its simple algorithm, high accuracy and less CPU time for solving the considered equation.