Related papers: SM stability for time-dependent problems
As the main contribution, this document provides a consistent discretization of a class of fixed-time stable systems, namely predefined-time stable systems. In the unperturbed case, the proposed approach allows obtaining not only a…
Based on our recent results, in this paper, a compact finite difference scheme is derived for a time fractional differential equation subject to the Neumann boundary conditions. The proposed scheme is second order accurate in time and…
Domain decomposition methods are used for approximate solving boundary problems for partial differential equations on parallel computing systems. Specific features of unsteady problems are taken into account in the most complete way in…
Inference for mechanistic models is challenging because of nonlinear interactions between model parameters and a lack of identifiability. Here we focus on a specific class of mechanistic models, which we term stable differential equations.…
Constraint tightening to non-conservatively guarantee recursive feasibility and stability in Stochastic Model Predictive Control is addressed. Stability and feasibility requirements are considered separately, highlighting the difference…
A class of finite difference schemes for solving a fractional anti-diffusive equation, recently proposed by Andrew C. Fowler to describe the dynamics of dunes, is considered. Their linear stability is analyzed using the standard Von Neumann…
An implicit finite difference scheme based on the $L2$-$1_{\sigma}$ formula is presented for a class of one-dimensional time fractional reaction-diffusion equations with variable coefficients and time drift term. The unconditional stability…
For solving two-dimensional incompressible flow in the vorticity form by the fourth-order compact finite difference scheme and explicit strong stability preserving (SSP) temporal discretizations, we show that the simple bound-preserving…
The rates of strong convergence for various approximation schemes are investigated for a class of stochastic differential equations (SDEs) which involve a random time change given by an inverse subordinator. SDEs to be considered are unique…
Preserving scalar boundedness is important for numerical schemes used in turbulent compressible multi-component flow simulations to prevent unphysical results and unstable simulations. However, ensuring scalar boundedness for high-order,…
The dynamical behavior of switched affine systems is known to be more intricate than that of the well-studied switched linear systems, essentially due to the existence of distinct equilibrium points for each subsystem. First, under…
A method is proposed for accurately describing arbitrary-shaped free boundaries in single-grid finite-difference schemes for elastodynamics, in a time-domain velocity-stress framework. The basic idea is as follows: fictitious values of the…
Finite element methods provide accurate and efficient methods for the numerical solution of partial differential equations by means of restricting variational problems to finite-dimensional approximating spaces. However, they do not…
In this paper, we numerically address the inverse problem of identifying a time-dependent coefficient in the time-fractional diffusion equation. An a priori estimate is established to ensure uniqueness and stability of the solution. A fully…
We establish sharp well-posedness and approximation estimates for variational saddle point systems at the continuous level. The main results of this note have been known to be true only in the finite dimensional case. Known spectral results…
We present a positive and asymptotic preserving numerical scheme for solving linear kinetic, transport equations that relax to a diffusive equation in the limit of infinite scattering. The proposed scheme is developed using a standard…
The need to smoothly cover a computational domain of interest generically requires the adoption of several grids. To solve the problem of interest under this grid-structure one must ensure the suitable transfer of information among the…
We study semi-dynamical systems associated to delay differential equations. We give a simple criteria to obtain weak and strong persistence and provide sufficient conditions to guarantee uniform persistence. Moreover, we show the existence…
This paper presents the generalized formulations of fundamental schemes for efficient unconditionally stable implicit finite-difference time-domain (FDTD) methods. The fundamental schemes constitute a family of implicit schemes that feature…
This paper is devoted to the complete convergence study of the finite-element approximation of Maxwell's equations in the case where the magnetic permeability is constant. Standard linear finite elements for the space discretization are…