Numerical Simulation and Dynamics of Burgers' Equation Using the Modified Cubic B-Spline Differential Quadrature Method

In the present work, a numerical approach using the Crank-Nicolson scheme along with the modified cubic B-spline differential quadrature (CN-MCDQ) method is proposed to find the numerical approximations to Burgers' equation. After applying the well-known Crank-Nicolson technique, Burgers' equation is solved in this study by using the differential quadrature approach to approximate the derivatives that lead to a system of equations to be solved. When compared to other methods for obtaining numerical solutions, the proposed method is shown to be efficient and easy to implement while still providing accurate results. The obtained results are in agreement with the earlier available approaches and are even better in comparison in terms of less domain partition. Three test problems were used to evaluate the methodology, and the results are tabulated and graphically shown below.