Numerical solutions of the modified Burgers’ equation by Petrov-Galerkin method

The modified Burgers’ equation (MBE) is solved numerically by the Petrov-Galerkin method using a linear hat function as the trial function and a cubic B-spline function as the test function. Product approximation has been used in this method. A linear stability analysis of the scheme shows it to be unconditionally stable. The accuracy of the presented method is demonstrated by two test problems. The numerical results are found in good agreement with the exact solutions.