##### Speaker

Alhsmy Trky, PhD student, Department of Mathematics and Statistics, MSU

##### Title

Mathematics Seminar Series

##### Subtitle

High-order adaptive exponential Runge-Kutta methods

##### Physical Location

Allen 411

##### Digital Location

https://msstate.webex.com/msstate/j.php?MTID=m9e5b618e666004aac2d307c0fd2e100f

**Abstract:** Exponential Runge-Kutta (ExpRK) methods have shown to be well-suited for the time discretization of stiff semilinear parabolic PDEs. The construction of stiffly-accurate ExpRK schemes requires solving a system of stiff order conditions which involve matrix functions. So far, methods up to order 5 have been derived by relaxing one or more order conditions (depending on a given order of accuracy). These schemes, however, allow using with constant stepsizes only. In this talk, we will derive new and efficient ExpRK schemes of high orders (up to order 6) which not only fulfill the stiff order conditions in the strong sense and but also support variable step sizes implementation. Numerical examples are given to verify the accuracy and to illustrate the efficiency of the newly constructed ExpRK schemes.

This is joint work with Vu Thai Luan.