Numerical Simulation of the Generalized Modified Benjamin-Bona-Mahony Equation Using SBP-SAT in Time

Sammanfattning: This paper describes simulations of the generalized modified Benjamin-Bona-Mahony (BBM) equation, using finite difference methods (FDM). Well-posed boundary conditions (BCs) as well as stable semi-discrete approximations are derived using summations-by-parts (SBP) operators combined with the projection method. For time integration, explicit Runge-Kutta 4 (RK4) is used, as well as SBP-SAT, which discretizes the temporal domain using SBP operators and imposes initial conditions using simultaneous approximation term (SAT). These time-marching methods are evaluated and compared in terms of accuracy and computing times, and soliton-boundary interaction is studied. It is shown that SBP-SAT time-marching perform well and is more suitable than RK4 for this type of non-linear, dispersive problem. Generalized summation-by-parts (GSBP) time-marching perform particularly well, due to high accuracy with few solution points.