Publication

Abstract : In this article, we develop and analyze an efficient numerical technique to solve the nonlinear temporal fractional Burgers’ equation (TFBE). The temporal fractional derivative is considered in the terms of Caputo and approximated by using the L2-1_{\sigma } scheme. The quintic B-spline (QBS) basis function is employed for discretization of the space derivative to obtain a fully discrete scheme. The proposed method is analyzed for its convergence and stability. Four nonlinear problems are considered to illustrate the advantage and applicability of the present method. The proposed scheme has an order of convergence O(\varDelta t^{2}+\varDelta x^4), where \varDelta t and \varDelta x are the step sizes in time and space directions, respectively. The comparison with the corresponding results of an existing method based on cubic parametric spline functions demonstrates that the proposed method is more accurate when solving the nonlinear time-fractional Burgers’ equation. The CPU time is provided to show the computational efficiency of the method. The obtained stable and highly-accurate numerical results and low computational time collectively underscore the significance of the proposed technique in solving the nonlinear time-fractional Burgers’ equation.