A collocation solution for Burgers' equation using cubic B-spline finite elements

Numerical solution of time fractional Burgers equation

“…[1]. Numerical solutions of the Burgers equation in the literature have been obtained using different methods and techniques [2,3,4,5,6,7]. In addition, the fractional order Burgers equation has been solved by many authors [8,9,10,11,12,13,14].…”

B-splines methods with redefined basis functions for solving fourth order parabolic partial differential equations

“…From the initial condition X(x, 0) on the function X(x, t) we must determine the initial vector c 0 , so that time evolution of c n , using (23) can be started [2].…”

A qualocation method for Burgers’ equation

“…123-127] and using appropriate compatibility conditions. Several numerical methods like finite difference methods [13], finite element methods [8], mixed finite element technique [9], Chebyshev spectral collocation methods in [5] and collocation procedures using cubic B-splines [2] are used to derive approximate solution to Burgers' equations. Bressan and Quarteroni have also discussed optimal error estimates in weighted L 2 -norm.…”