Preconditioned Implicit-Exponential (IMEXP) Time Integrators for Stiff Differential Equations
This work addresses the computational bottleneck of exponential integrators for stiff DEs by enabling flexible preconditioner use, which is an incremental improvement over existing methods.
The authors propose new IMEXP and hybrid exponential time integrators for stiff differential equations that allow the use of any preconditioner, improving computational efficiency and broadening applicability. Numerical results demonstrate stability and convergence.
We propose two new classes of time integrators for stiff DEs: the implicit-explicit exponential (IMEXP) and the hybrid exponential methods. In contrast to the existing exponential schemes, the new methods offer significant computational advantages when used with preconditioners. Any preconditioner can be used with any of these new schemes. This leads to a broader applicability of exponential methods. The proof of stability and convergence of these integrators and numerical demonstration of their efficiency are presented.