Strang splitting method to Benjamin-Bona-Mahony type equations: Analysis and application

We provide an error analysis of operator splitting for equations of the type ut−∂x2ut=Au+12∂x(u2), where A is an unbounded linear differential operator such that the equation is well-posed. Two particular examples are generalized Benjamin-Bona-Mahony and KdV-BBM equations. A second order error bound of the Strang splitting method in time is proved under suitable regularity assumptions on the exact solution. Finally, the orders of convergence are checked by two numerical experiments and the errors are presented.