Related papers: The Stochastic TR-BDF2 Scheme of Order 2
We use the linear scalar SDE as a test problem to show that it is possible to construct almost sure stable first-order weak balanced schemes based on the addition of stabilizing functions to the drift terms. Then, we design balanced schemes…
Context: Calculating stellar pulsations requires a sufficient accuracy to match the quality of the observations. Many current pulsation codes apply a second order finite-difference scheme, combined with Richardson extrapolation to reach…
Optimization in Deep Learning is mainly dominated by first-order methods which are built around the central concept of backpropagation. Second-order optimization methods, which take into account the second-order derivatives are far less…
We consider stochastic approximation with block-coordinate stepsizes and propose adaptive stepsize rules that aim to minimize the expected distance from the next iterate to an (unknown) target point. These stepsize rules employ online…
This paper introduces an adaptive time splitting technique for the solution of stiff evolutionary PDEs that guarantees an effective error control of the simulation, independent of the fastest physical time scale for highly unsteady…
The Kolmogorov-Petrovsky-Piskunov (Fisher-KPP) equation is a classical reaction-diffusion equation with broad applications such as biology, chemistry and physics. In this paper, an alternative second-order scheme is proposed by employing a…
In this paper, we present an error estimate of a second-order linearized finite element (FE) method for the 2D Navier-Stokes equations with variable density. In order to get error estimates, we first introduce an equivalent form of the…
This paper addresses the safe stabilization problem of stochastic nonlinear time-delay systems. Based on theKrasovskii approach, we first propose a stochastic control Lyapunov-Krasovskii functional to guarantee the stabilization objective…
Second-order macroscopic continuum models have been constantly improving for decades to reproduce the empirical observations. Recently, a series of experimental studies have suggested that the stochastic factors contribute significantly to…
Conventional finite-difference schemes for solving partial differential equations are based on approximating derivatives by finite-differences. In this work, an alternative theory is proposed which view finite-difference schemes as…
An unsteady problem is considered for a space-fractional equation in a bounded domain. A first-order evolutionary equation involves the square root of an elliptic operator of second order. Finite element approximation in space is employed.…
Two-time-scale optimization is a framework introduced in Zeng et al. (2024) that abstracts a range of policy evaluation and policy optimization problems in reinforcement learning (RL). Akin to bi-level optimization under a particular type…
In this paper, we obtain results on exponential stability of second order delay differential equations, which are based on a version of the Floquet theory for delay differential equations of the second order we proposed. Our version allows…
In this work, we present a second-order nonuniform time-stepping scheme for the time-fractional Allen-Cahn equation. We show that the proposed scheme preserves the discrete maximum principle, and by using the convolution structure of…
In this paper we provide a detailed convergence analysis for an unconditionally energy stable, second-order accurate convex splitting scheme for the Modified Phase Field Crystal equation, a generalized damped wave equation for which the…
We propose a second-order time to collision (TTC) considering non-static acceleration and turning with realistic assumptions. This is equivalent to considering that the steering wheel is held at a fixed angle with constant pressure on the…
In this paper, a second order finite difference scheme is investigated for time-dependent one-side space fractional diffusion equations with variable coefficients. The existing schemes for the equation with variable coefficients have…
We consider a class of stochastic gradient optimization schemes. Assuming that the objective function is strongly convex, we prove weak error estimates which are uniform in time for the error between the solution of the numerical scheme,…
In this paper, a third-order time adaptive algorithm with less computation, low complexity is provided for shale reservoir model based on coupled fluid flow with porous media flow. The algorithm combines the three-step linear time filters…
This paper investigates the two-dimensional stochastic steady-state Navier-Stokes(NS) equations with additive random noise. We introduce an innovative splitting method that decomposes the stochastic NS equations into a deterministic NS…