Applied Math Colloquium: Vu Thai Luan (Texas Tech University)

Title: Innovative time integrators for stiff and highly oscillatory problems

Abstract: In this talk, we present two new classes of innovative time integration methods for stiff and highly oscillatory systems. For first-order stiff evolution problems or parabolic PDEs (e.g., diffusion-reaction systems), we introduce exponential Hermite-type methods. For second-order problems or hyperbolic PDEs (e.g., wave equations), we introduce exponential Nyström integrators. Under reasonable regularity assumptions, we prove convergence results up to fifth-order accuracy for these methods, with error bounds that remain independent of the stiffness or high-frequency components of the problem. Numerical experiments demonstrate the accuracy and efficiency of these new methods compared to existing widely-used schemes in the literature.

https://www.depts.ttu.edu/math/facultystaff/bio.php?id=1803