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) …

Our understanding of magnetic reconnection (MR) under chromospheric conditions remains
limited. Recent observations have demonstrated the important role of ion–neutral …

In this paper we introduce a family of explicit Runge-Kutta methods, referred to as Paired
Explicit Runge-Kutta (P-ERK) schemes, that are suitable for the solution of stiff systems of …

Abstract A multilevel Monte Carlo (MLMC) method for mean square stable stochastic
differential equations with multiple scales is proposed. For such problems, that we call stiff …

We investigate implicit–explicit (IMEX) general linear methods (GLMs) with inherent Runge–
Kutta stability (IRKS) for differential systems with non-stiff and stiff processes. The …

In this work, we aim at constructing numerical schemes, that are as efficient as possible in
terms of cost and conservation of invariants, for the Vlasov–Fokker–Planck system coupled …

Context. The scientific community employs complicated multiphysics simulations to
understand the physics in solar, stellar, and interstellar media. These must be tested against …

A second-order L-stable exponential time-differencing (ETD) method is developed by
combining an ETD scheme with approximating the matrix exponentials by rational functions …

Stabilized Runge–Kutta methods are especially efficient for the numerical solution of large
systems of stiff nonlinear differential equations because they are fully explicit. For semi …

Explicit stabilized methods are an efficient alternative to implicit schemes for the time
integration of stiff systems of differential equations in large dimension. In this paper we …