Extended modified cubic B-spline algorithm for nonlinear Burgers' equation

In this paper, an extended modified cubic B-Spline differential quadrature method is proposed to approximate the solution of the nonlinear Burgers' equation. The proposed method is used in space and a five-stage and four order strong stability-preserving time-stepping Runge-Kutta (SSP-RK54) method is used in time. The accuracy and efficiency of the method is illustrated by considering four numerical problems. The numerical results of the method are compared with some existing methods and it was found that the proposed numerical method produces acceptable results and even more accurate results in comparison with some existing methods. The stability analysis of the scheme is also carried out and was found to be unconditionally stable.