Resumen de A vibrating string with dynamic frictionless impact

Jeongho Ahn

• In this paper, we consider the wave equation with unilateral constraints, which describes the transverse motion of vibrating string with fixed ends impacting a stationary rigid obstacle. Conservation of energy is investigated. Convergence of the numerical trajectories in both semi-discrete case and fully-discrete case is proved. The numerical scheme is implemented with the complementarity problem that arises in the numerical method being solved, using the Fischer-Burmeister function. Our numerical results provide evidence of energy conservation with some particular shapes of obstacle.