Black hole (BH) accretion flows and jets are dynamic hot relativistic magnetized plasma
flows whose radiative opacity can significantly affect flow structure and behaviour. We …

We consider implicit-explicit (IMEX) Runge--Kutta (RK) schemes for hyperbolic systems with
stiff relaxation in the so-called diffusion limit. In such a regime the system relaxes towards a …

Spatial discretizations of time-dependent partial differential equations usually result in a
large system of semi-linear and stiff ordinary differential equations. Taking the structures into …

This article aims at developing a high order pressure-based solver for the solution of the 3D
compressible Navier-Stokes system at all Mach numbers. We propose a cell-centered …

The main purpose of the paper is to show how to use implicit–explicit Runge–Kutta methods
in a much more general context than usually found in the literature, obtaining very effective …

In this article we present a high order cell-centered numerical scheme in space and time for
the solution of the compressible Navier-Stokes equations. To deal with multiscale …

Here we investigate global strong solutions for a class of partially dissipative hyperbolic
systems in the framework of critical homogeneous Besov spaces. Our primary goal is to …

A review of diagonally implicit Runge-Kutta (DIRK) methods applied to rst-order ordinary di
erential equations (ODEs) is undertaken. The goal of this review is to summarize the …

We discuss implicit-explicit (IMEX) Runge--Kutta methods which are particularly adapted to
stiff kinetic equations of Boltzmann type. We consider both the case of easy invertible …

Two new implicit–explicit, additive Runge–Kutta (ARK 2) methods are given with fourth-and
fifth-order formal accuracies, respectively. Both combine explicit Runge–Kutta (ERK) …