Solving non-linear problems by complex time step methods

Recently, a new type of time step integration algorithms using complex time steps has been proposed. For linear problems, the algorithms are higher order accurate, unconditionally stable and have directly controllable numerical dissipation. Solutions with high accuracy can be generated using large time steps. In this paper, the algorithms are extended to solve non-linear problems. The pseudo-force approach is adopted in treating the non-linear terms. To maintain the solutions accuracy, the pseudo-force is reconstructed by interpolation. Special treatments are required to compute the excitation at the complex time steps. Several numerical examples are analysed. It is observed that the complex time step method can be computationally more efficient than the Newmark method when very accurate numerical solutions are required. Copyright (C) 2002 John Wiley Sons, Ltd.