DE Seminar: Sylvia Amihere (UMBC)

Title: Embedded Implicit-Explicit Strong Stability Preserving Runge--Kutta Methods

Abstract: Strong Stability Preserving (SSP) Runge-Kutta methods are time integration schemes designed to preserve monotonicity and nonlinear stability properties of spatial discretization methods when solving time-dependent differential equations.  In recent times, new classes of problems have emerged which can be modeled by time-dependent equations that involve both stiff and non-stiff terms, where the non-stiff terms are solved explicitly and stiff terms are treated implicitly. This has motivated the development of Implicit-Explicit (ImEx) SSP methods designed for fixed time stepping. However, this may not be ideal for problems with rapidly changing dynamics. To address this limitation, we introduce a new class of ImEx SSP methods that employ adaptive time stepping to adjust step sizes while preserving stability properties. Numerical experiments are conducted to analyze the efficiency and robustness of these new methods.