Related papers: Mass-Matrix Differential-Algebraic Equation Formul…
In this paper, pseudo-transient continuation method has been modified and implemented in power system long-term stability analysis. This method is a middle ground between integration and steady state calculation, thus is a good compromise…
We consider a linear scalar delay differential equation (DDE), consisting of two arbitrary distributed time delays. We formulate necessary conditions for stability of the trivial solution which are independent of the distributions. For the…
We proposed a provably stable FDTD subgridding method for accurate and efficient transient electromagnetic analysis. In the proposed method, several field components are properly added to the boundaries of Yee's grid to make sure that the…
Two combined numerical methods for solving semilinear differential-algebraic equations (DAEs) are obtained and their convergence is proved. The comparative analysis of these methods is carried out and conclusions about the effectiveness of…
Forecasting physical signals in long time range is among the most challenging tasks in Partial Differential Equations (PDEs) research. To circumvent limitations of traditional solvers, many different Deep Learning methods have been…
We present an energy-stable scheme for numerically approximating the governing equations for incompressible two-phase flows with different densities and dynamic viscosities for the two fluids. The proposed scheme employs a scalar-valued…
A boundary integral equation (BIE) formulation for 2-D transient elastic wave propagation problems is presented. On the basis of the three-dimensional integral identity, the time-dependent kernels for the two-dimensional boundary integral…
Transient stability assessment is an integral part of dynamic security assessment of power systems. Traditional methods of transient stability assessment, such as time domain simulation approach and direct methods, are appropriate for…
Dynamical systems that are subject to continuous uncertain fluctuations can be modelled using Stochastic Differential Equations (SDEs). Controlling such system results in solving path constrained SDEs. Broadly, these problems fall under the…
The method and the formula of variation of constants for ordinary differential equations (ODEs) is a fundamental tool to analyze the dynamics of an ODE near an equilibrium. It is natural to expect that such a formula works for delay…
This paper deals with stability of discrete-time switched linear systems whose all subsystems are unstable. We present sufficient conditions on the subsystems matrices such that a switched system is globally exponentially stable under a set…
Differentiable models of physical systems provide a powerful platform for gradient-based algorithms, with particular impact on parameter estimation and optimal control. Quantum systems present a particular challenge for such…
Interconnection and damping assignment passivity-based control scheme has been used to stabilize many physical systems such as underactuated mechanical systems through total energy shaping. In this method, some partial differential…
Motivated by the advantages achieved by implicit analogue net for solving online linear equations, a novel implicit neural model is designed based on conventional explicit gradient neural networks in this letter by introducing a…
In multiple access channels (MAC), multiple users share a transmission medium to communicate with a common receiver. Traditional constellations like quadrature amplitude modulation are optimized for point-to-point systems and lack…
In recent years, kinetic equations have been used to model many social phenomena. A key feature of these models is that transition rate kernels involve Dirac delta functions, which capture sudden, discontinuous state changes. Here, we study…
We are interested in the numerical solution of nonsymmetric linear systems arising from the discretization of convection-diffusion partial differential equations with separable coefficients and dominant convection. Preconditioners based on…
In this paper, some adaptive single-step methods like Trapezoid (TR), Implicit-mid point (IMP), Euler-backward (EB), and Radau IIA (Rad) methods are implemented in Maple to solve index-1 nonlinear Differential Algebraic Equations (DAEs).…
The Partial Integral Equation (PIE) framework was developed to computationally analyze linear Partial Differential Equations (PDEs) where the PDE is first converted to a PIE and then the analysis problem is solved by solving operator-valued…
The dynamics of power grids are governed by a large number of nonlinear differential and algebraic equations (DAEs). To safely operate the system, operators need to check that the states described by these DAEs stay within prescribed limits…