Abstract
This paper deals with the design and analysis of a high order numerical scheme for the nonlinear time-fractional generalized Fisher's equation (TFGFE). The Caputo fractional derivative (FD) of order alpha, (alpha is an element of (0, 1)) appearing in the model problem is approximated by means of L1 - 2 scheme. The discretization for the space derivative is made by a collocation method based on quintic B-spline (QBS) basis function. Convergence analysis of the method is established. Five examples are provided to demonstrate the efficiency and feasibility of the method. The influence of alpha on the solution profile of the TFGFE is examined. It is shown that our method is of O(Delta t(2) + Delta x(4)) accuracy, where Delta t and Delta x respectively represent the time and space step sizes. The results obtained are compared with those of other three methods. The CPU time (in seconds) is given in order to justify the computational efficiency of proposed numerical scheme. (C) 2021 Elsevier B.V. All rights reserved.
NSTL
Elsevier