Numerical solution of Burgers’ equation by cubic Hermite collocation method

• CHCM eliminates continuity condition of trial function and its derivative.
• Variation of accuracy with the different choice of collocation points.
• Present technique reduces the computational work due to continuity properties.

In this paper, numerical solution of the non-linear Burgers’ equation are obtained by using cubic Hermite collocation method (CHCM). The advantage of the method is continuity of the dependent variable and its derivative throughout the solution range. A linear stability analysis shows that the numerical scheme based on Crank–Nicolson approximation in time is unconditionally stable. This method is applied on some test problems, with different choice of collocation points to validate the accuracy of the method. The obtained numerical results show that the method is efficient, robust and reliable even for high Reynolds numbers, for which the exact solution fails. Moreover, the method can be applied to a wide class of nonlinear partial differential equations.