Cubic B-spline collocation method for solving Benjamin-Bona-Mahony equation

Abstract

In this research, the Benjamin-Bona-Mahony equation is solved numerically using cubic B-spline (CBS) collocation method. Forward difference approximation is used to discretize the time derivative while the CBS function is used to discretize the space dimension. To deal with nonlinearity, the nonlinear term is replaced with a known parameter. At every time level, calculations are repeated two or three times to increase the accuracy of the results. Applying von-Neumann stability analysis, the proposed technique is shown to be unconditionally stable under Crank-Nicolson scheme. Comparison of the numerical results is done with the results from some recent schemes.