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.