Complex-time-step methods for transient analysis

Unconditionally stable time step integration algorithms with controllable numerical dissipation of arbitrary order of accuracy are presented for transient analysis. The algorithms are based on the h-method for "rst-order di!erential equations. The results at several (complex) sub-step locations are evaluated and combined linearly to give higher-order accurate results at the end of a time step. The ampli"cation factors are shown to be related to the PadeH approximations to the exponential function. The computational procedures for parabolic and hyperbolic problems are discussed. The interpolation procedure for the solutions within a time step is given. Numerical examples are used to illustrate the validity of the present complex-time-step algorithms.