相关论文: Refactorization of a variable step, unconditionall…

We propose a novel second order in time numerical scheme for Cahn-Hilliard-Navier- Stokes phase field model with matched density. The scheme is based on second order convex-splitting for the Cahn-Hilliard equation and pressure-projection…

We show that accelerated gradient descent, averaged gradient descent and the heavy-ball method for non-strongly-convex problems may be reformulated as constant parameter second-order difference equation algorithms, where stability of the…

We consider ultraweak variational formulations for (parametrized) linear first order transport equations in time and/or space. Computationally feasible pairs of optimally stable trial and test spaces are presented, starting with a suitable…

We extend nonparametric regression smoothing splines to a context where there is endogeneity and instrumental variables are available. Unlike popular existing estimators, the resulting estimator is one-step and relies on a unique…

We analyze a variable-step extension of a family of arbitrarily high-order exponential time differencing multistep (ETD-MS) schemes recently developed by the authors. We prove that the schemes are unconditionally stable in the sense that a…

A new, improved split-step backward Euler (SSBE) method is introduced and analyzed for stochastic differential delay equations(SDDEs) with generic variable delay. The method is proved to be convergent in mean-square sense under conditions…

We prove that the two-step backward differentiation formula (BDF2) method is stable on arbitrary time grids; while the variable-step BDF3 scheme is stable if almost all adjacent step ratios are less than 2.553. These results relax the…

To address the magnetization dynamics in ferromagnetic materials described by the Landau-Lifshitz-Gilbert equation under large damping parameters, a third-order accurate numerical scheme is developed by building upon a second-order method…

In this note we shall devise a variable-order continuous Galerkin time stepping method which is especially geared towards norm-preserving dynamical systems. In addition, we will provide an a posteriori estimate for the $L^\infty$-error.

In this paper, we propose a new numerical strategy for the stabilization of evolution systems. The method is based on the methodology given by Ammari, Nicaise andPignotti in ''Stabilization by switching time-delay, Asymptot. Anal., 83…

Several results regarding the stability and the stabilization of linear impulsive positive systems under arbitrary, constant, minimum, maximum and range dwell-time are obtained. The proposed stability conditions characterize the pointwise…

Sequential Monte Carlo methods have been a major breakthrough in the field of numerical signal processing for stochastic dynamical state-space systems with partial and noisy observations. However, these methods still present certain…

We present stochastic variants of the exponential time differencing schemes for stiff stochastic differential equations. We derive three explicit schemes that offer better stability compared to Euler-Maruyama and Milstein's method, and…

Recent applications (e.g. active gels and self-assembly of elastic sheets) motivate the need to efficiently simulate the dynamics of thin elastic sheets. We present semi-implicit time stepping algorithms to improve the time step constraints…

Motivated by their broad applications in reinforcement learning, we study the linear two-time-scale stochastic approximation, an iterative method using two different step sizes for finding the solutions of a system of two equations. Our…

The explicit two-stage fourth-order (TSFO) temporal-spatial coupling method is efficient and compact but suffers severe time-step restrictions for stiff problems with multiple scales. To address Professor Jiequan Li's call for an implicit…

Pre-filtering and post-filtering steps can be added to many of the traditional numerical methods to generate new, higher order methods with strong stability properties. Presented in this paper are a variable step pre-filter and post-filter…

We carry out a stability and convergence analysis of a fully discrete scheme for the time-dependent Navier-Stokes equations resulting from combining an $H(\mathrm{div}, \Omega)$-conforming discontinuous Galerkin spatial discretization, and…

We study the stability properties of explicit marching schemes for second-kind Volterra integral equations that arise when solving boundary value problems for the heat equation by means of potential theory. It is well known that explicit…

We analyze the problem of fitting a fonction en escalier or multi-step function to a curve in L^2 Hilbert space. We propose a two-stage optimization approach whereby the step positions are initially fixed, corresponding to a classic linear…