Unconditionally stable implicit time-marching methods are powerful in efficiently solving stiff differential equations. In this talk, I will present a novel unified framework for handling both physical and numerical stiffness based on Time-Accurate and highly-Stable Explicit (TASE) operators.
The proposed TASE operators act as preconditioners on the stiff terms and can be readily deployed to most existing explicit time-marching methods. The resulting time integration method remains the original explicit time-marching schemes, yet with nearly unconditional stability. The TASE operators can be designed to be arbitrarily high-order accurate such that the original explicit time-marching accuracy order is preserved. I will illustrate the performance of the TASE method on a set of benchmark problems with strong stiffness. Numerical results demonstrate that the proposed framework preserves the high-order accuracy of the explicit time-marching methods with very-large time steps for all the considered cases.