Restricted Padé scheme in computational structural dynamics

Restricted Padé schemes Rmp where the denominator is a complete power p of a linear function have been examined analytically by Nörsett. Here this method is evaluated with paying special attention to numerical aspects when solving typical finite-element systems in structural dynamics with n degrees of freedom and with essential properties like sparsety and symmetry. This paper presents an efficient implicit restricted time-stepping scheme R22 with a final coefficient matrix of order n and a leading error term proportional to h4. This is a significant improvement compared with the most popular Padé-P11-Newmark scheme with matrix order n, too, but error term h3 on the one hand and the well established Padé-P12-discontinuous Hamiltonian approach with error term h4 but matrix order 2×n on the other hand. The classical P11-scheme and the new restricted R22-scheme are compared in a modal manner and by assessing the correlation between local error estimator and global error.