In recent years, the SUite of Nonlinear and DIfferential/ALgebraic equation Solvers
(SUNDIALS) has been redesigned to better enable the use of application-specific and third …

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) …

We derive a formulation of the nonhydrostatic equations in spherical geometry with a Lorenz
staggered vertical discretization. The combination conserves a discrete energy in exact time …

We describe the ARKODE library of one-step time integration methods for ordinary
differential equation (ODE) initial-value problems (IVPs). In addition to providing standard …

We conduct a thorough study of different forms of horizontally explicit and vertically implicit
(HEVI) time-integration strategies for the compressible Euler equations on spherical …

Abstract The nonhydrostatic High‐Order Method Modeling Environment (HOMME‐NH)
atmospheric dynamical core supports acoustic waves that propagate significantly faster than …

We propose entropy-preserving and entropy-stable partitioned Runge–Kutta (RK) methods.
In particular, we extend the explicit relaxation Runge–Kutta methods to IMEX–RK methods …

The next-generation atmospheric dynamics model for numerical weather prediction and
climate studies is developed at INM RAS and Hydrometcentre of Russia. The model uses a …

We construct and analyze a second-order implicit–explicit (IMEX) scheme for the time
integration of semilinear second-order wave equations. The scheme treats the stiff linear …

A high‐order‐accurate weighted essentially non‐oscillatory (WENO) limited upwind finite‐
volume scheme is detailed for the compressible, nonhydrostatic, inviscid Euler equations …