Related papers: A New Implicit-Explicit Local Method to Capture St…
We present a method for determining optimal modes of operation for autonomously oscillating systems with uncertain parameters. In a typical application of the method, a nonlinear dynamical system is optimized with respect to an economic…
In this paper we classify the pathwise asymptotic behaviour of the discretisation of a general autonomous scalar differential equation which has a unique and globally stable equilibrium. The underlying continuous equation is subjected to a…
We study step-wise time approximations of non-linear hyperbolic initial value problems. The technique used here is a generalization of the minimizing movements method, using two time-scales: one for velocity, the other (potentially much…
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…
We propose in this paper efficient first/second-order time-stepping schemes for the evolutional Navier-Stokes-Nernst-Planck-Poisson equations. The proposed schemes are constructed using an auxiliary variable reformulation and sophisticated…
Recently, a new class of BDF schemes proposed in [F. Huang and J. Shen, SIAM J Numer. Anal., 62.4, 1609--1637] for the parabolic type equations are studied in this paper. The basic idea is based on the Taylor expansions at time…
This study proposes a method for designing stabilizing suboptimal controllers for nonlinear stochastic systems. These systems include time-invariant stochastic parameters that represent uncertainty of dynamics, posing two key difficulties…
A wide range of implicit time integration methods, including multi-step, implicit Runge-Kutta, and Galerkin finite-time element schemes, is evaluated in the context of chaotic dynamical systems. The schemes are applied to solve the Lorenz…
We introduce a family of implicit probabilistic integrators for initial value problems (IVPs), taking as a starting point the multistep Adams-Moulton method. The implicit construction allows for dynamic feedback from the forthcoming…
The main goal of this paper is to investigate the order reduction phenomenon that appears in the integral deferred correction (InDC) methods based on implicit-explicit (IMEX) Runge-Kutta (R-K) schemes when applied to a class of stiff…
In this article we propose a new adaptive numerical quadrature procedure which includes both local subdivision of the integration domain, as well as local variation of the number of quadrature points employed on each subinterval. In this…
We present a new efficient computational approach for time-dependent first-order Hamilton-Jacobi-Bellman PDEs. Since our method is based on a time-implicit Eulerian discretization, the numerical scheme is unconditionally stable, but…
This paper investigates the simultaneous identification of a spatially dependent potential and the initial condition in a subdiffusion model based on two terminal observations. The existence, uniqueness, and conditional stability of the…
In this work, we explore various relevant aspects of the Smoothed Particle Hydrodynamics regarding Burger's equation. The stability, precision, and efficiency of the algorithm are investigated in terms of different implementations. In…
Policy iteration is one of the classical frameworks of reinforcement learning, which requires a known initial stabilizing control. However, finding the initial stabilizing control depends on the known system model. To relax this requirement…
We report on recent work on adaptive timestep control for weakly instationary gas flows [16, 18, 17] carried out within SFB 401, TPA3. The method which we implement and extend is a space-time splitting of adjoint error representations for…
An adaptive BDF2 implicit time-stepping method is analyzed for the phase field crystal model. The suggested method is proved to preserve a modified energy dissipation law at the discrete levels if the time-step ratios…
This paper considers a two-step fourth-order modified explicit Euler/Crank-Nicolson numerical method for solving the time-variable fractional mobile-immobile advection-dispersion model subjects to suitable initial and boundary conditions.…
Standard stochastic optimization methods are brittle, sensitive to stepsize choices and other algorithmic parameters, and they exhibit instability outside of well-behaved families of objectives. To address these challenges, we investigate…
We propose a general methodology of sequential locally optimal design of experiments for explicit or implicit nonlinear models, as they abound in chemical engineering and, in particular, in vapor-liquid equilibrium modeling. As a sequential…