Related papers: Implicit-explicit methods based on strong stabilit…
Dynamical systems with sub-processes evolving on many different time scales are ubiquitous in applications. Their efficient solution is greatly enhanced by automatic time step variation. This paper is concerned with the theory, construction…
The analysis of strong-stability-preserving (SSP) linear multistep methods is extended to semi-discretized problems for which different terms on the right-hand side satisfy different forward Euler (or circle) conditions. Optimal additive…
We consider the Cahn-Hilliard equation with standard double-well potential. We employ a prototypical class of first order in time semi-implicit methods with implicit treatment of the linear dissipation term and explicit extrapolation of the…
We present a class of new explicit and stable numerical algorithms to solve the spatially discretized linear heat or diffusion equation. After discretizing the space and the time variables like conventional finite difference methods, we do…
Neural PDE solvers offer a powerful tool for modeling complex dynamical systems, but often struggle with error accumulation over long time horizons and maintaining stability and physical consistency. We introduce a multiscale implicit…
Many low-Mach or all-Mach number codes are based on space discretizations which in combination with the first order explicit Euler method as time integration would lead to an unstable scheme. In this paper, we investigate how the choice of…
This study presents an efficient, accurate, effective and unconditionally stable time stepping scheme for the Darcy-Brinkman equations in double-diffusive convection. The stabilization within the proposed method uses the idea of stabilizing…
In this work we study different Implicit-Explicit (IMEX) schemes for incompressible flow problems with variable viscosity. Unlike most previous work on IMEX schemes, which focuses on the convective part, we here focus on treating parts of…
We present an original study on the numerical stabiliy of explicit schemes solving the incompressible Euler equations on an open domain with slipping boundary conditions. Relying on the skewness property of the non-linear term, we…
The stability of nonlinear explicit difference schemes with not, in general, open domains of the scheme operators are studied. For the case of path-connected, bounded, and Lipschitz domains, we establish the notion that a multi-level…
An extension of the two-step staggered time discretization of linear elastodynamics in stress-velocity form to systems involving internal variables subjected to a possibly non-linear dissipative evolution is proposed. The original scheme is…
We present compact semi-implicit finite difference schemes on structured grids for numerical solutions of the advection by an external velocity and by a speed in normal direction that are applicable in level set methods. The most involved…
In this work, we propose a nonlinear stabilization technique for scalar conservation laws with implicit time stepping. The method relies on an artificial diffusion method, based on a graph-Laplacian operator. It is nonlinear, since it…
In this paper, uniformly unconditionally stable first and second order finite difference schemes are developed for kinetic transport equations in the diffusive scaling. We first derive an approximate evolution equation for the macroscopic…
We consider hyperbolic systems of conservation laws with relaxation source terms leading to a diffusive asymptotic limit under a parabolic scaling. We introduce a new class of secondorder in time and space numerical schemes, which are…
This paper introduces new model parameterizations for learning discrete-time dynamical systems from data via the Koopman operator and studies their properties. Whereas most existing works on Koopman learning do not take into account the…
Hyperexponential stability is investigated for dynamical systems with the use of both, explicit and implicit, Lyapunov function methods. A nonlinear hyperexponential control is designed for stabilizing linear systems. The tuning procedure…
We propose second-order implicit-explicit (IMEX) time-stepping schemes for nonlinear fractional differential equations with fractional order $0<\beta<1$. From the known structure of the non-smooth solution and by introducing corresponding…
We consider a finite element method with symmetric stabilisation for the discretisation of the transient convection--diffusion equation. For the time-discretisation we consider either the second order backwards differentiation formula or…
Review of implicit methods of integrating system of stiff ordinary differential equations is presented. Defines and graphically presents absolute stability region for Gears methods (backward differentiation formula) used to solve system of…