An implicit family of time marching procedures with adaptive dissipation control

In this work, an unconditionally stable family of time marching procedures is proposed, in which the time integration parameters of the method are locally computed, considering the properties of the model. Thus, the technique adapts to the characteristics of the problem, enabling enhanced analyses. Here, adaptive dissipation control is explored, allowing spurious modes to be more effectively dissipated. The proposed technique is second-order accurate, L-stable, truly self-starting and very easy to implement. Numerical results are presented along the paper, illustrating the good performance of the novel single-step technique.