Higher-order accurate time-step-integration algorithms by post-integration techniques

In this paper, a framework to construct higher-order-accurate time-step-integration algorithms based on the post-integration techniques is presented. The prescribed initial conditions are naturally incorporated in the formulations and can be strongly or weakly enforced. The algorithmic parameters are chosen such that unconditionally A-stable higher-order-accurate time-step-integration algorithms with controllable numerical dissipation can be constructed for linear problems. Besides, it is shown that the order of accuracy for non-linear problems is maintained through the relationship between the present formulation and the Runge–Kutta method. The second-order di;erential equations are also considered. Numerical examples are given to illustrate the validity of the present formulation