Exponential integrators have received a lot of attention in recent years as a viable alternative to implicit schemes for stiff systems. In particular, there has been a surge of interest in the exponential propagation iterative Runge-Kutta (EPIRK) framework. However, open source implementation of the algorithms is lacking at the moment. This project aims to add state-of-the-art exponential Runge-Kutta integrators to JuliaDiffEq's solver repertoire, which can benefit both algorithm developers and researchers who need efficient solvers for stiff problems. Main challenges for the project include the evaluation of high-order phi-functions, the transition from semilinear to generic systems and time step adaptation for the integrators.

Organization

Student

Xingjian Guo

Mentors

  • Mike Innes
  • Christopher Rackauckas
close

2018