Convergence of a spectral Galerkin scheme for the dynamic elastica with periodical or hinged boundary

Abstract

For the dynamic elastica with the quasi-periodic or the hinged boundary conditions, a spectral Galerkin scheme is presented for approximating the smooth solution. It is established that the scheme enjoys a spectral and second order accuracy with respect to the size of the spatial and temporal grid, respectively. Moreover, some results of numerical experiments are given to examine the convergence of discrete solutions to the corresponding exact solutions.