Application of the B-spline Galerkin approach for approximating the time-fractional Burger's equation

Abstract

<abstract> <p>This paper presents a numerical scheme based on the Galerkin finite element method and cubic B-spline base function with quadratic weight function to approximate the numerical solution of the time-fractional Burger's equation, where the fractional derivative is considered in the Caputo sense. The proposed method is applied to two examples by using the $L_2$ and $ {L_\infty } $ error norms. The obtained results are compared with a previous existing method to test the accuracy of the proposed method.</p> </abstract>