TY - JOUR
TI - A Jacobi wavelet collocation method for fractional fisher's equation in time
AU - Secer Aydin
AU - Cinar Melih
JN - Thermal Science
PY - 2020
VL - 24
IS - 11
SP - 119
EP - 129
PT - Article
AB - 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.