Discrete transparent boundary conditions for the equation of rod transverse vibrations
Local perturbations of an infinitely long rod travel to infinity. On the contrary, in the case of a finite length of the rod, the perturbations reach its boundary and are reflected. The boundary conditions constructed here for the implicit difference scheme imitate the Cauchy problem and provide almost no reflection. These boundary conditions are non- local with respect to time, and their practical implementation requires additional calcu- lations at every time step. To minimise them, a special rational approximation, similar to the Hermite - Padé approximation is used. Numerical experiments confirm the high “transparency”of these boundary conditions and determine the conditional stability regions for finite-difference scheme.