High-fidelity numerical simulation of the dynamic beam equation

high-fidelity finite difference approximation of the dynamic beam equation is derived. Different types of well-posed boundary conditions are analysed. The boundary closures are based on the summation-by-parts (SBP) framework and the boundary conditions are imposed using a penalty (SAT) technique, to guarantee linear stability. The resulting SBP-SAT approximation leads to fully explicit time integration. The accuracy and stability properties of the newly derived SBP-SAT approximations are demonstrated for both 1-D and 2-D problems.