Related papers: Numerical stability for finite difference approxim…
In this paper, we discuss the time-space Caputo-Riesz fractional diffusion equation with variable coefficients on a finite domain. The finite difference schemes for this equation are provided. We theoretically prove and numerically verify…
We consider linear dynamical systems consisting of ordinary differential equations with high dimensionality. The aim of model order reduction is to construct an approximating system of a much lower dimension. Therein, the reduced system may…
High-order accurate, $\textit{entropy stable}$ numerical methods for hyperbolic conservation laws have attracted much interest over the last decade, but only a few rigorous convergence results are available, particularly in multiple space…
In this work, we study of the algebraic-hyperbolic formulation of the Einstein constraint equations for numerically constructing initial data sets for inhomogeneous cosmological space-times with $\mathbb{T}^3$ topology. We implement a…
In the harmonic description of general relativity, the principle part of Einstein's equations reduces to 10 curved space wave equations for the componenets of the space-time metric. We present theorems regarding the stability of several…
We present two families of first-order in time and second-order in space formulations of the Einstein equations (variants of the Arnowitt-Deser-Misner formulation) that admit a complete set of characteristic variables and a conserved energy…
We revisit the numerical stability of four well-established explicit stochastic integration schemes through a new generic benchmark stochastic differential equation designed to assess asymptotic statistical accuracy and stability…
This paper studies a class of random nonlinear systems with time-varying delay, in which the $r$-order moment ($r\geq1$) of the random disturbance is finite. Firstly, some general conditions are proposed to guarantee the existence and…
We consider hyperbolic systems of conservation laws with relaxation source terms leading to a diffusive asymptotic limit under a parabolic scaling. We introduce a new class of secondorder in time and space numerical schemes, which are…
This paper provides a new unified framework for second-moment stability of discrete-time linear systems with stochastic dynamics. Relations of notions of second-moment stability are studied for the systems with general stochastic dynamics,…
Along the general framework of the gauge-invariant perturbation theory developed in the papers [K. Nakamura, Prog. Theor. Phys. {\bf 110} (2003), 723; {\it ibid}, {\bf 113} (2005), 481.], we re-derive the second-order Einstein equations on…
There is a tendency to write the equations of general relativity as a first order symmetric system of time dependent partial differential equations. However, for numerical reasons, it might be advantageous to use a second order formulation…
This work deals with Lipschitz stability for a parametric version of the general second order Ordinary Differential Equation (ODE) initial-value Cauchy problem. We first establish a Lipschitz stability result for this problem under a…
We investigate the relevance of the conformal method by investigating stability issues for the Einstein-Lichnerowicz conformal constraint system in a nonlinear scalar-field setting. We prove the stability of the system with respect to…
In this paper, we investigate the inverse quasi-variational inequality problem in finite-dimensional spaces. First, we introduce a second-order dynamical system whose trajectory converges exponentially to the solution of the inverse…
We extend the definition of $n$-dimensional difference equations to complex order $\alpha\in \mathbb{C} $. We investigate the stability of linear systems defined by an $n$-dimensional matrix $A$ and derive conditions for the stability of…
We develop a framework to give upper bounds on the "practical" computational complexity of stability problems for a wide range of nonlinear continuous and hybrid systems. To do so, we describe stability properties of dynamical systems using…
The stability properties of the Einstein Static solution of General Relativity are altered when corrective terms arising from modification of the underlying gravitational theory appear in the cosmological equations. In this paper the…
We investigate the dynamical stability of the holographic system with two order parameters, which exhibits competition and coexistence of condensations. In the linear regime, we have developed the gauge dependent formalism to calculate the…
We study a second order BDF (Backward Differentiation Formula) scheme for the numerical approximation of parabolic HJB (Hamilton-Jacobi-Bellman) equations. The scheme under consideration is implicit, non-monotone, and second order accurate…