Improving stability domains of the implicit higher order accuracy method

The implicit higher order accuracy (IHOA) time integration family has a high order of accuracy. However, its stability domains are very restrictive. By improving the stability conditions, the larger time steps can be utilized. In this study, two parameters are introduced in the displacement and velocity extrapolations of IHOA. In order to find the optimum values of the proposed parameters, the dissipation and the dispersion are investigated. Three conditionally stable versions of the second‐, third‐, and forth‐order algorithms are found. It is shown that these formulations have larger stability domains than the previous ones. Furthermore, the suggested strategies give responses that are more accurate. Copyright © 2011 John Wiley & Sons, Ltd.