Numerical simulation of the generalized modified Benjamin–Bona–Mahony equation using SBP-SAT in time - Kjelldahl, Vilma; Mattsson, Ken (Journal of computational and applied mathematics, 2025)
In this paper we present high-order accurate finite difference approximations for solving the generalized modified Benjamin–Bona–Mahony (BBM) equation, a non-linear soliton model. The spatial discretization uses high-order accurate summation-by-parts (SBP) finite difference operators combined with both weak and strong enforcement of boundary conditions. For time integration we compare the explicit RK4 method against an implicit SBP time integrator. These time-marching methods are evaluated and compared in terms of accuracy and efficiency. It is shown that the implicit SBP time-integrator is more efficient than the explicit RK4 method for non-linear soliton models. •Stable approximations of the generalized modified BBM equation are derived.•An implicit SBP-SAT temporal discretization is derived.•The SBP-SAT temporal discretization, as compared to RK4, is much more efficient.•SBP-Projection is a more favourable method of imposing BC, as compared to SAT.