Related papers: Uniform accuracy of implicit-explicit Runge-Kutta …
Problems that feature significantly different time scales, where the stiff time-step restriction comes from a linear component, implicit-explicit (IMEX) methods alleviate this restriction if the concern is linear stability. However, where…
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 with Poisson or Amp\`ere equation. Splitting methods…
In this paper, we present a framework to construct general stochastic Runge-Kutta Lawson schemes. We prove that the schemes inherit the consistency and convergence properties of the underlying Runge-Kutta scheme, and confirm this in some…
We consider the development of high order asymptotic-preserving linear multistep methods for kinetic equations and related problems. The methods are first developed for BGK-like kinetic models and then extended to the case of the full…
Identifying governing equations in physical and biological systems from datasets remains a long-standing challenge across various scientific disciplines, providing mechanistic insights into complex system evolution. Common methods like…
We show that, even for extremely stiff systems, explicit integration may compete in both accuracy and speed with implicit methods if algebraic methods are used to stabilize the numerical integration. The required stabilizing algebra depends…
We consider the application of Runge-Kutta (RK) methods to gradient systems $(d/dt)x = -\nabla V(x)$, where, as in many optimization problems, $V$ is convex and $\nabla V$ (globally) Lipschitz-continuous with Lipschitz constant $L$.…
We present unconditionally energy stable Runge-Kutta (RK) discontinuous Galerkin (DG) schemes for solving a class of fourth order gradient flows. Our algorithm is geared toward arbitrarily high order approximations in both space and time,…
Explicit stabilized methods are highly efficient time integrators for large and stiff systems of ordinary differential equations especially when applied to semi-discrete parabolic problems. However, when local spatial mesh refinement is…
This paper studies fixed-step convergence of implicit-explicit general linear methods. We focus on a subclass of schemes that is internally consistent, has high stage order, and favorable stability properties. Classical, index-1…
In this paper we develop a class of Implicit-Explicit Runge-Kutta schemes for solving the multi-scale semiconductor Boltzmann equation. The relevant scale which characterizes this kind of problems is the diffusive scaling. This means that,…
We present an approach for the efficient implementation of self-adjusting multi-rate Runge-Kutta methods and we introduce a novel stability analysis, that covers the multi-rate extensions of all standard Runge-Kutta methods and allows to…
New time integration methods are proposed for simulating incompressible multiphase flow in pipelines described by the one-dimensional two-fluid model. The methodology is based on 'half-explicit' Runge-Kutta methods, being explicit for the…
The effects of kinetic-energy preservation errors due to Runge-Kutta (RK) temporal integrators have been analyzed for the case of large-eddy simulations of incompressible turbulent channel flow. Simulations have been run using the…
In this paper we study the stability of explicit finite difference discretizations of linear advection-diffusion equations (ADE) with arbitrary order of accuracy in the context of method of lines. The analysis first focuses on the stability…
We propose a unified theoretical framework to examine the energy dissipation properties at all stages of explicit exponential Runge-Kutta (EERK) methods for gradient flow problems. The main part of the novel framework is to construct the…
Traditional time discretization methods use a single timestep for the entire system of interest and can perform poorly when the dynamics of the system exhibits a wide range of time scales. Multirate infinitesimal step (MIS) methods (Knoth…
This paper deals with stability of classical Runge-Kutta collocation methods. When such methods are embedded in linearly implicit methods as developed in [12] and used in [13] for the time integration of nonlinear evolution PDEs, the…
In this paper the analysis of an asymptotic preserving (AP) IMEX-RK finite volume scheme for the wave equation system in the zero Mach number limit is presented. The accuracy of a numerical scheme at low Mach numbers is its ability to…
Many astrophysical processes involving magnetic fields and quasi-stationary processes are well described when assuming the fluid as a perfect conductor. For these systems, the ideal-magnetohydrodynamics (MHD) description captures the…