Related papers: Consistency Analysis of Finite Difference Approxim…
We consider a Navier-Stokes fluid-plate interaction (FSI) system which describes the evolutions of the fluid contained within a 3D cavity, as it interacts with a deformable elastic membrane on the ``free" upper boundary of the cavity. These…
This paper presents and analyzes two robust, efficient, and optimally accurate fully discrete finite element algorithms for computing the parameterized Navier-Stokes Equations (NSEs) flow ensemble. The timestepping algorithms are…
An exact discretization method is being developed for solving linear systems of ordinary fractional-derivative differential equations with constant matrix coefficients (LSOFDDECMC). It is shown that the obtained linear discrete system in…
In this paper, a linearized semi-implicit finite difference scheme is proposed for solving the two-dimensional (2D) space fractional nonlinear Schr\"{o}dinger equation (SFNSE).The scheme has the property of mass and energy conservation on…
The Residual Smooting Scheme (RSS) have been introduced in \cite{AverbuchCohenIsraeli} as a backward Euler's method with a simplified implicit part for the solution of parabolic problems. RSS have stability properties comparable to those of…
We study systems on time scales that are generalizations of classical differential or difference equations. In this paper we consider linear systems and their small nonlinear perturbations. In terms of time scales and of eigenvalues of…
In this work, a novel second-order nonstandard finite difference (NSFD) method that preserves simultaneously the positivity and local asymptotic stability of one-dimensional autonomous dynamical systems is introduced and analyzed. This…
In this work stability results for systems described by coupled Retarded Functional Differential Equations (RFDEs) and Functional Difference Equations (FDEs) are presented. The results are based on the observation that the composite system…
The compact finite difference method is a powerful tool for discretizing conservation laws, owing to its inherent flexibility in developing high-resolution and highly stable schemes. In this paper, we propose a framework for the design of…
In this work, we investigate the numerical approximation of the second order non-autonomous semilnear parabolic partial differential equation (PDE) using the finite element method. To the best of our knowledge, only the linear case is…
We propose a new method to design adaptation algorithms that guarantee a certain prescribed level of performance and are applicable to systems with nonconvex parameterization. The main idea behind the method is, given the desired…
Neural ordinary differential equations (NODE) have been recently proposed as a promising approach for nonlinear system identification tasks. In this work, we systematically compare their predictive performance with current state-of-the-art…
We study the basic computational problem of detecting approximate stationary points for continuous piecewise affine (PA) functions. Our contributions span multiple aspects, including complexity, regularity, and algorithms. Specifically, we…
Dynamic systems are ubiquitous in nature and are used to model many processes in biology, chemistry, physics, medicine, and engineering. In particular, systems of ordinary differential equations are commonly used for the mathematical…
We present in this paper a pressure correction scheme for barotropic compressible Navier-Stokes equations, which enjoys an unconditional stability property, in the sense that the energy and maximum-principle-based a priori estimates of the…
This paper presents a finite-dimensional approximation for a class of partial differential equations on the space of probability measures. These equations are satisfied in the sense of viscosity solutions. The main result states the…
Over the centuries mathematicians have been challenged by the partial differential equations (PDEs) that describe the motion of fluids in many physical contexts. Important and beautiful results were obtained in the past one hundred years,…
Finite difference schemes are the method of choice for solving nonlinear, degenerate elliptic PDEs, because the Barles-Sougandis convergence framework [Barles and Sougandidis, Asymptotic Analysis, 4(3):271-283, 1991] provides sufficient…
We study convergence of a finite volume scheme for the compressible (barotropic) Navier--Stokes system. First we prove the energy stability and consistency of the scheme and show that the numerical solutions generate a dissipative…
Neural Stochastic Differential Equations (NSDEs) model the drift and diffusion functions of a stochastic process as neural networks. While NSDEs are known to make accurate predictions, their uncertainty quantification properties have been…