Error Estimates of the Fourier Collocation Combined Strang Splitting Method for Benjamin-Bona-Mahony Type Equations

In this paper, we present an optimal-order global error analysis for the fully discretized scheme of theBenjamin–Bona–Mahony (BBM) type equations. The BBM equation is splitted into two parts: linear and nonlinear parts. Then the Strang splitting method is applied in time while the Fourier collocation method is studied for space discretization. Semi-discrete and fully discrete Fourier collocation schemes are constructed. The convergence of the fully discretized scheme is established using the global time discretization error and the Fourier interpolation error, under appropriate regularity assumptions on the exact solution. To support the obtained theoretical results and to demonstrate the effectiveness of the proposed method, four illustrative examples have been studied. In addition, the performance of the method has been examined on a single soliton wave equation, where the corresponding mass, energy and momentum values are presented to show that the scheme is preserved.