The power of chemistry to prepare new molecules and materials has driven the quest for
new approaches to solve problems having global societal impact, such as in renewable …

Kinetic and hyperbolic equations contain small scales (mean free path/time, Debye length,
relaxation or reaction time, etc.) that lead to various different asymptotic regimes, in which …

This book deals with numerical methods for solving partial differential equa tions (PDEs)
coupling advection, diffusion and reaction terms, with a focus on time-dependency. A …

We consider new implicit–explicit (IMEX) Runge–Kutta methods for hyperbolic systems of
conservation laws with stiff relaxation terms. The explicit part is treated by a strong-stability …

Additive Runge–Kutta (ARK) methods are investigated for application to the spatially
discretized one-dimensional convection–diffusion–reaction (CDR) equations. Accuracy …

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 …

A new method for the parallelization of numerical methods for partial differential equations
(PDEs) in the temporal direction is presented. The method is iterative with each iteration …

In this article, we propose a new class of finite volume schemes of arbitrary accuracy in
space and time for systems of hyperbolic balance laws with stiff source terms. The new class …

A semi-implicit formulation of the method of spectral deferred corrections (SISDC) for
ordinary differential equations with both stiff and non-stiff terms is presented. Several …

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 …