相关论文: On a C2-nonlinear subdivision scheme avoiding Gibb…

In this paper, we are concerned with the stabilization of linear port-Hamiltonian systems of arbitrary order $N \in \mathbb{N}$ on a bounded $1$-dimensional spatial domain $(a,b)$. In order to achieve stabilization, we couple the system to…

This paper presents a new approach and methodology to solve the second order one dimensional hyperbolic telegraph equation with Dirichlet and Neumann boundary conditions using the cubic trigonometric B-spline collocation method. The usual…

This paper provides approximation orders for a class of nonlinear interpolation procedures for univariate data sampled over $\sigma$ quasi-uniform grids. The considered interpolation is built using both essentially nonoscillatory (ENO) and…

A general algorithm is presented for estimating the nonlinear instability threshold, $\sigma_c$, for subcritical transitions in systems where the linearized dynamics is significantly non-normal (i.e. subcritical bifurcations of {\em…

We study the oscillations and stability of self-gravitating cylindrically symmetric fluid systems and collisionless systems. This is done by studying small perturbations to the equilibrium system and finding the normal modes, using methods…

We propose and analyze a linearly stabilized semi-implicit diffusive Crank--Nicolson scheme for the Cahn--Hilliard gradient flow. In this scheme, the nonlinear bulk force is treated explicitly with two second-order stabilization terms. This…

A transition to unsteadiness of a flow inside a cubic diagonally lid-driven cavity with no-slip boundaries is numerically investigated by a series of direct numerical simulations (DNS) performed on 100^3 and 200^3 stretched grids. It is…

This paper is devoted to study the limit cycle problem of a cubic reversible system with an isochronous center, when it is perturbed inside a class of polynomials. An upper bound of the number of limit cycles is obtained using the Abelian…

We propose and study a new multilevel method for the numerical approximation of a Gibbs distribution $\pi$ on $\mathbb{R}^d$, based on (overdamped) Langevin diffusions. This method inspired by \cite{mainPPlangevin} and…

Hausel and Rodriguez-Villegas recently observed that work of G\"ottsche, combined with a classical result of Erd\H{o}s and Lehner on integer partitions, implies that the limiting Betti distribution for the Hilbert schemes…

Focusing on a two-field Swift-Hohenberg model with linear nonreciprocal interactions, this study investigates how emerging higher-codimension points act as organizing centers for the nonequilibrium phase diagram that features various steady…

We consider a general class of two-dimensional spin systems, with continuous but not necessarily smooth, possibly long-range, $O(N)$-symmetric interactions, for which we establish algebraically decaying upper bounds on spin-spin…

In recent years, Neural Networks (NNs) have been employed to control nonlinear systems due to their potential capability in dealing with situations that might be difficult for conventional nonlinear control schemes. However, to the best of…

We present a novel approach for the inverse problem in electrical impedance tomography based on regularized quadratic regression. Our contribution introduces a new formulation for the forward model in the form of a nonlinear integral…

We present a novel structure-preserving numerical scheme for discontinuous finite element approximations of nonlinear hyperbolic systems. The method can be understood as a generalization of the Lax-Friedrichs flux to a high-order staggered…

The high-order numerical solution of the non-linear shallow water equations (and of hyperbolic systems in general) is susceptible to unphysical Gibbs oscillations that form in the proximity of strong gradients. The solution to this problem…

In this paper, two kinds of high-order compact finite difference schemes for second-order derivative are developed. Then a second-order numerical scheme for Riemann-Liouvile derivative is established based on fractional center difference…

We study Langevin-type algorithms for sampling from Gibbs distributions such that the potentials are dissipative and their weak gradients have finite moduli of continuity not necessarily convergent to zero. Our main result is a…

We consider the defocusing nonlinear Schr\"odinger equations on the two-dimensional compact Riemannian manifold without boundary or a bounded domain in $\R^2$. Our aim is to give a pedagogic and self-contained presentation on the Wick…

We provide a new upper bound for sampling numbers $(g_n)_{n\in \mathbb{N}}$ associated to the compact embedding of a separable reproducing kernel Hilbert space into the space of square integrable functions. There are universal constants…