NUMERICAL SOLUTION OF BBM-BURGER EQUATION WITH QUARTIC B-SPLINE COLLOCATION METHOD

The present article is concerned with the numerical solution of Benjamin-Bona-Mahony-Burgers (BBM-Burger) equation by quartic B-spline collocation method. The method is based on quartic B-spline basis functions for space integration, and Crank-Nicolson formulation for time integration. Numerical examples considered by different researchers are discussed to illustrate the efficiency, robustness and reliability of the proposed method. Unconditional stability of the proposed method for BBM-Burger equation has been discussed and demonstrated by using von-Neumann method. The computed numerical solutions are in good agreement with the results available in literature as well as with exact solutions. The proposed scheme needs less storage space and execution time hence can be easily implemented to solve equations existing in various physical models.