Related papers: Von Neumann Stability Analysis for Multi-level Mul…
The companion paper "Higher-order in time quasi-unconditionally stable ADI solvers for the compressible Navier-Stokes equations in 2D and 3D curvilinear domains", which is referred to as Part I in what follows, introduces ADI (Alternating…
We consider a class of Riemannian optimization problems where the objective is the sum of a smooth function and a nonsmooth function, considered in the ambient space. This class of problems finds important applications in machine learning…
Diffusion and flow-driven instability, or transport-driven instability, is one of the central mechanisms to generate inhomogeneous gradient of concentrations in spatially distributed chemical systems. However, verifying the transport-driven…
Despite significant advancements in out-of-distribution (OOD) detection, existing methods still struggle to maintain robustness against adversarial attacks, compromising their reliability in critical real-world applications. Previous…
Advection-Diffusion-Reaction (ADR) Partial Differential Equations (PDEs) appear in a wide spectrum of applications such as chemical reactors, concentration flows, and biological systems. A large number of these applications require the…
This paper introduces a new method for assessing the boundedness and stability of certain vector nonlinear systems with delays and variable coefficients. The approach is based on developing scalar counterparts to the given vector systems.…
This paper presents a novel application of multiparameter spectral theory to the study of structural stability, with particular emphasis on aeroelastic flutter. Methods of multiparameter analysis allow the development of new solution…
A stability analysis is performed on high-order schemes formulated using the Flux Reconstruction (FR) approach. The one-dimensional advection model equation is used for the assessment of the stability region of these schemes when coupled…
Differential dynamic programming (DDP) is a popular technique for solving nonlinear optimal control problems with locally quadratic approximations. However, existing DDP methods are not designed for stochastic systems with unknown…
We consider fully discrete schemes based on the scalar auxiliary variable (SAV) approach and stabilized SAV approach in time and the Fourier-spectral method in space for the phase field crystal (PFC) equation. Unconditionally energy…
In this study, novel exact solutions of the Duffing equation with their phase portraits have been proposed and reasoned. It is shown that phase trajectories are initially elliptical and become distorted in the unstable area within the…
Recently, there has been an increasing interest in using tools from dynamical systems to analyze the behavior of simple optimization algorithms such as gradient descent and accelerated variants. This paper strengthens such connections by…
We perform a von Neumann stability analysis on a common discretization of the Einstein equations. The analysis is performed on two formulations of the Einstein equations, namely, the standard ADM formulation and the conformal-traceless (CT)…
This paper develops validated computational methods for studying infinite dimensional stable manifolds at equilibrium solutions of parabolic PDEs, synthesizing disparate errors resulting from numerical approximation. To construct our…
Understanding the quasi-static fracture formation and evolution is essential for assessing the mechanical properties and structural load-bearing capacity of materials. Peridynamics (PD) provides an effective computational method to depict…
We present a new stability and error analysis of fully discrete approximation schemes for the transient Stokes equation. For the spatial discretization, we consider a wide class of Galerkin finite element methods which includes both inf-sup…
The von Neumann entropy of a graph is a spectral complexity measure that has recently found applications in complex networks analysis and pattern recognition. Two variants of the von Neumann entropy exist based on the graph Laplacian and…
This paper develops a robust dynamic mode decomposition (RDMD) method endowed with statistical and numerical robustness. Statistical robustness ensures estimation efficiency at the Gaussian and non-Gaussian probability distributions,…
This paper focuses on the mathematical approaches to the analysis of stability that is a crucial step in the design of dynamical systems. Three methods are presented, namely, absolutely integrable impulse response, Fourier integral, and…
Estimation of the degree of stability and the bounds of solutions to non-autonomous nonlinear systems present major concerns in numerous applied problems. Yet, current techniques are frequently yield overconservative conditions which are…