Convergence analysis and numerical solution of the Benjamin–Bona–Mahony equation by Lie–Trotter splitting

Abstract

In this paper, an operator splitting method is used to analyze nonlinear Benjamin–Bona–Mahony-typeequations. We split the equation into an unbounded linear part and a bounded nonlinear part and then Lie–Trottersplitting is applied to the equation. The local error bounds are obtained by using the approach based on the differentialtheory of operators in a Banach space and the quadrature error estimates via Lie commutator bounds. The global errorestimate is obtained via Lady Windermere’s fan argument. Finally, to confirm the expected convergence order, numericalexamples are studied.