DMS Applied and Computational Mathematics Seminar

Title: On energy laws and stability of Runge-Kutta methods for linear seminegative problems

Abstract: In scientific and engineering applications, people usually encounter time-dependent systems with a decaying total energy. A natural question to ask is that when using a time integration method to approximate such systems, whether and how the energy-decay law will be preserved at the discrete level. In this talk, we will focus on linear autonomous systems and present a general framework on deriving discrete energy identities for both explicit and implicit Runge-Kutta (RK) method. The established identities provide a precise characterization on energy generation or dissipation in the RK discretization, thereby leading to weak and strong stability criteria of RK methods. Furthermore, we also present a general energy identity for all the diagonal Padé approximations, based on an analytical Cholesky type decomposition of a class of symmetric matrices.