Trigonometric tension B-spline collocation approximations for time fractional Burgers’ equation

Abstract

This manuscript’s aim is to form and examine the numerical simulation of Caputo-time fractional nonlinear Burgers’ equation via collocation approach with trigonometric tension B-splines as base functions. First, L1 discretization formula is utilized for the time fractional derivative and after linearizing the nonlinear term, the trigonometric tension B-spline interpolants are utilized to get a system of simultaneous linear equations that are solved via Gauss elimination method. Thus, numerical approximation at the desired time level is obtained. It is demonstrated via von-Neumann approach that proposed scheme produces stable solutions. The results of six different test examples having their analytical solutions are compared with the results in the literature to validate the accuracy and efficiency of the scheme.