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For many systems of differential equations modeling problems in science and engineering, there are natural splittings of the right hand side into two parts, one non-stiff or mildly stiff, and the other one stiff. For such systems…

Numerical Analysis · Computer Science 2013-04-09 Angelamaria Cardone , Zdzislaw Jackiewicz , Hong Zhang , Adrian Sandu

The incompressible Euler equations are an important model system in computational fluid dynamics. Fast high-order methods for the solution of this time-dependent system of partial differential equations are of particular interest: due to…

Numerical Analysis · Mathematics 2024-10-15 Eike Hermann Müller

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…

Numerical Analysis · Mathematics 2016-03-06 Giacomo Dimarco , Lorenzo Pareschi

In this article we design a finite volume semi-implicit IMEX scheme for the incompressible Navier-Stokes equations on evolving Chimera meshes. We employ a time discretization technique that separates explicit and implicit terms which…

Numerical Analysis · Mathematics 2023-08-08 Michele Giuliano Carlino , Walter Boscheri

This study focuses on the development and analysis of a group of high-order implicit-explicit (IMEX) Runge--Kutta (RK) methods that are suitable for discretizing gradient flows with nonlinearity that is Lipschitz continuous. We demonstrate…

Numerical Analysis · Mathematics 2024-03-22 Zhaohui Fu , Tao Tang , Jiang Yang

We present an implicit-explicit (IMEX) scheme for semilinear wave equations with strong damping. By treating the nonlinear, nonstiff term explicitly and the linear, stiff part implicitly, we obtain a method which is not only unconditionally…

Numerical Analysis · Mathematics 2024-07-01 Daniel Eckhardt , Marlis Hochbruck , Barbara Verfürth

In this work we construct a high-order Asymptotic-Preserving (AP) Implicit-Explicit (IMEX) scheme for the ES-BGK model for gas mixtures introduced in [Brull, Commun. Math. Sci., 2015]. The time discretization is based on the IMEX strategy…

Numerical Analysis · Mathematics 2025-12-01 Domenico Caparello , Lorenzo Pareschi , Thomas Rey

In this work, we focus on the development of high-order Implicit-Explicit (IMEX) finite volume numerical methods for plasmas in quasineutral regimes. At large temporal and spatial scales, plasmas tend to be quasineutral, meaning that the…

Numerical Analysis · Mathematics 2024-09-10 Nicolas Crouseilles , Giacomo Dimarco , Saurav Samantaray

Singularly perturbed systems (SPSs) are prevalent in engineering applications, where numerically solving their initial value problems (IVPs) is challenging due to stiffness arising from multiple time scales. Classical explicit methods…

Numerical Analysis · Mathematics 2025-04-15 Yibo Shi , Cristian R. Rojas

We propose a new method that extends conservative explicit multirate methods to implicit explicit-multirate methods. We develop extensions of order one and two with different stability properties on the implicit side. The method is suitable…

Numerical Analysis · Mathematics 2021-12-21 Emil M. Constantinescu

Low-rank methods for kinetic equations have attracted increasing attention due to their effectiveness in reducing the high dimensionality of phase space. In our previous work [G. Wang & J. Hu, J. Comput. Phys. 558 (2026) 114884], we…

Numerical Analysis · Mathematics 2026-05-18 Geshuo Wang , Jingwei Hu

Implicit-explicit Runge-Kutta (IMEX-RK) time discretization methods are very popular when solving stiff kinetic equations. In [21], an asymptotic analysis shows that a specific class of high-order IMEX-RK schemes can accurately capture the…

Numerical Analysis · Mathematics 2026-01-12 Sebastiano Boscarino , Seung Yeon Cho

The context of this work is the development of first order total variation diminishing (TVD) implicit-explicit (IMEX) Runge-Kutta (RK) schemes as a basis of a Multidimensional Optimal Order detection (MOOD) approach to approximate the…

Numerical Analysis · Mathematics 2025-01-08 Victor Michel-Dansac , Andrea Thomann

In this paper, we propose a new high order semi-implicit scheme for the all Mach full Euler equations of gas dynamics. Material waves are treated explicitly, while acoustic waves are treated implicitly, thus avoiding severe CFL restrictions…

Numerical Analysis · Mathematics 2021-10-28 Sebastiano Boscarino , Jing-Mei Qiu , Giovanni Russo , Tao Xiong

A simple iterative approach for solving a set of implicit kinetic moment equations is proposed. This implicit solve is a key component in the IMEX discretization of the multi-species Bhatnagar-Gross-Krook (M-BGK) model with nontrivial…

Numerical Analysis · Mathematics 2024-04-30 Evan Habbershaw , Cory D. Hauck , Steven M. Wise

Efficient long-time integration of nonlinear fractional differential equations is significantly challenging due to the integro-differential nature of the fractional operators. In addition, the inherent non-smoothness introduced by the…

Numerical Analysis · Mathematics 2019-09-11 Yongtao Zhou , Jorge L. Suzuki , Chengjian Zhang , Mohsen Zayernouri

We propose an optimization proxy in terms of iterative implicit gradient methods for solving constrained optimization problems with nonconvex loss functions. This framework can be applied to a broad range of machine learning settings,…

Optimization and Control · Mathematics 2025-10-14 Harshal D. Kaushik , Ming Jin

This paper proposes a theoretical framework for establishing the energy dissipation of general implicit-explicit linear multistep methods (IMEX-LMMs) for gradient flows, by constructing a dissipative modified energy consisting of the…

Numerical Analysis · Mathematics 2026-05-27 Chaoyu Quan , Huaijin Wang , Xuping Wang , Chuanju Xu

In this paper, two novel classes of implicit exponential Runge-Kutta (ERK) methods are studied for solving highly oscillatory systems. First of all, we analyze the symplectic conditions of two kinds of exponential integrators, and present a…

Numerical Analysis · Mathematics 2023-12-05 Xianfa Hu , Wansheng Wang , Bin Wang , Yonglei Fang

In this paper we continue the work on implicit-explicit (IMEX) time discretizations for the incompressible Oseen equations that we started in \cite{BGG23} (E. Burman, D. Garg, J. Guzm\`an, {\emph{Implicit-explicit time discretization for…

Numerical Analysis · Mathematics 2024-05-22 Erik Burman , Deepika Garg , Johnny Guzman