An efficient higher-order trigonometric cubic B-spline collocation method for timefractional Burgers equations

Abstract This manuscript is devoted to investigate the numerical solutions of the nonlinear time-fractional Burgers equation representing a significant extension of the classical Burgers equation to fractional derivative. For this purpose, an efficient higher-order trigonometric cubic B-spline collocation method which is based on finite element analysis presented and used to achieve the aim of the manuscript. During the obtaining the numerical solutions of the mentioned equation, the discretization of the spatial part is performed via Crank-Nicolson approach and the time derivative is performed in Caputo sense and discretization of the time derivative is made by L 1 algorithm. Also, the nonlinear term seen in the Burgers equation is linearized through the use of Rubin-Graves linearization technique. Consequently, the performing of the collocation method is resulted to obtain a numerical scheme which is producing an algebraic system being solved by iteratively. The stability of the numerical scheme is investigated using von-Neumann stability criteria. Three test problems are considered to confirm the validity, accuracy and efficiently of the method. The error between numerical solutions and exact ones is measured with the norms L 2 and L ∞ . Comparisons results are presented by tables, the behaviour of the numerical solutions and the harmony with the exact solutions are depicted with graphs as well.