Hyperbolic systems with stiff relaxation constitute a wide class of evolutionary partial
differential equations which describe several physical phenomena, ranging from gas …

We prove that the two-step backward differentiation formula (BDF) method is stable on
arbitrary time grids; while the variable-step three-step backward differentiation formula …

Excerpt This book focuses on IMEX methods, with particular emphasis on their application to
systems of PDEs. IMEX methods have proven to be highly effective for solving a wide range …

Many hyperbolic and kinetic equations contain a non-stiff convection/transport part and a stiff
relaxation/collision part (characterized by the relaxation or mean free time $\varepsilon $) …

This is one of our series works on discrete energy analysis of the variable-step BDF
schemes. In this part, we present stability and convergence analysis of the third-order BDF …

Implicit-explicit Runge-Kutta (IMEX-RK) schemes are popular methods to treat multiscale
equations that contain a stiff part and a non-stiff part, where the stiff part is characterized by a …

With the rapid advance of Machine Learning techniques and the deep increase of
availability of scientific data, data-driven approaches have started to become progressively …

In this paper, uniformly unconditionally stable first and second order finite difference
schemes are developed for kinetic transport equations in the diffusive scaling. We first derive …

Geometrical complexity is typical of missile and reentry systems, small-scale devices with
intrinsic milli-to-micro scale features, or in general topology-rich systems. Additionally, at …

In this paper, a multiscale constitutive framework for one-dimensional blood flow modeling is
presented and discussed. By analyzing the asymptotic limits of the proposed model, it is …