Home
I'm an applied mathematician who has worked on many things ranging from fluids, hydrodynamic stability, operations research, electromagnetism. I'm always seeking inovative methods.
Recently I have been developing and implementing a new time-step method for stiff ODEs which I call the SIMEX method. It stands for "shortcut implicit-explict" method. Implicit-explicit methods (IMEX) are frequently used with Runge-Kutta and multi-step methods in many scientific applications. The shortcut version of an IMEX method has the remarkable property that it does not require an accurate solution of the implicit equation.
This is great news because it allows iterative solvers to be stopped as soon as time-step stability is reached. The SIMEX method can be used with multi-step methods and also with a large class of Runge-Kutta methods. More details about the SIMEX method can be found in this preprint "A shortcut for IMEX methods: integrate the residual explicitly".