An Exponential Cubic B-spline Algorithm for the Nonlinear Coupled Burgers' Equation

Abstract

The collocation method based on the exponential cubic B-splines (ECB-splines) together with the Crank-Nicolson formula is used to solve nonlinear coupled Burgers' equation (CBE). This method is tested by studying three different problems. The proposed scheme is compared with some existing methods. textbf{It produced accurate results }with the suitable selection of the free parameter of the ECB-spline function. It produces accurate results. Stability of the fully discretized CBE is investigated by the Von Neumann analysis.