Third order complex-time-step methods for transient analysis Original Research Article

Using complex-time-steps and the θ-method for the first order differential equations, third order accurate A-stable step-by-step time integration algorithms with controllable numerical dissipation are constructed for transient analysis. The results at two sub-step locations are evaluated and combined linearly with the corresponding weighting factors to give higher order accurate results at the end of a time-step. The sub-step locations and the weighting factors are complex numbers. The amplification factors at infinity are controlled by another algorithmic parameter μ. A fourth order accurate algorithm is obtained when μ=1. The algorithmic characteristics and the computational procedure for the present third order algorithms are discussed. Equivalent algorithms and comparisons with other algorithms are given. The present algorithms are found to be competitive with the other third and fourth order accurate algorithms.