A simple and effective single‐step time marching technique based on adaptive time integrators

In this work, a novel time marching procedure is presented in which adaptive time integration parameters are locally computed, allowing different spatial and temporal distributions. As a consequence, a more versatile technique arises, enabling an enhanced performance. The main features of the proposed technique are: (1) it is simple; (2) it has guaranteed stability; (3) it is an efficient non‐iterative adaptive single‐step procedure; (4) it provides enhanced accuracy; (5) it enables advanced controllable algorithmic dissipation in the higher modes; (6) it is truly self‐starting; and (7) it is entirely automatic, requiring no input parameter from the user. The proposed technique is very complete, providing the main positive attributes that are requested from an effective time marching procedure. Numerical results are presented along the paper, illustrating the excellent performance of the method. Copyright © 2016 John Wiley & Sons, Ltd.