Related papers: Equivalent Systems for Differential Equations with…
Incorporating symmetries into the numerical solution of differential equations has been a mainstay of research over the last 40 years, however, one aspect is less known and under-utilised: discretisations of partial differential equations…
This paper addresses the challenging numerical simulation of nonlinear hybrid stochastic functional differential equations with infinite delays. We first propose an explicit scheme using space and time truncation, requiring only finite…
The differential equations involving two discrete delays are helpful in modeling two different processes in one model. We provide the stability and bifurcation analysis in the fractional order delay differential equation $D^\alpha x(t)=a…
Traditionally, the delay margin of a looped system is computed by considering both the controller and system representations that evolve in the same space (e.g. either continuous or discrete-time). However, as in practice the system is…
We develop in this work a numerical method for stochastic differential equations (SDEs) with weak second order accuracy based on Gaussian mixture. Unlike the conventional higher order schemes for SDEs based on It\^o-Taylor expansion and…
We present a proof of concept for solving a 1+1D complex-valued, delay partial differential equation (PDE) that emerges in the study of waveguide quantum electrodynamics (QED) by adapting the finite-difference time-domain (FDTD) method. The…
In this article we develop a new methodology to prove weak approximation results for general stochastic differential equations. Instead of using a partial differential equation approach as is usually done for diffusions, the approach…
A distributed discrete-time algorithm is proposed for multi-agent networks to achieve a common least squares solution of a group of linear equations, in which each agent only knows some of the equations and is only able to receive…
For a wide class of polynomially nonlinear systems of partial differential equations we suggest an algorithmic approach to the s(trong)-consistency analysis of their finite difference approximations on Cartesian grids. First we apply the…
A general method of obtaining linear differential equations having polynomial solutions is proposed. The method is based on an equivalence of the spectral problem for an element of the universal enveloping algebra of some Lie algebra in the…
A characteristic matrix function captures the spectral information of a bounded linear operator in a matrix-valued function. In this article, we consider a delay differential equation with one discrete time delay and assume this equation is…
In this paper, we present experimental algorithms for solving the dualization problem. We present the results of extensive experimentation comparing the execution time of various algorithms.
In [7], a new iterative method for solving linear system of equations was presented which can be considered as a modification of the Gauss-Seidel method. Then in [4] a different approach, say 2D-DSPM, and more effective one was introduced.…
We study abstract linear and nonlinear evolutionary systems with single or multiple delay feedbacks, illustrated by several concrete examples. In particular, we assume that the operator associated with the undelayed part of the system…
Fractional derivative and delay are important tools in modeling memory properties in the natural system. This work deals with the stability analysis of a fractional order delay differential equation \begin{equation*} D^\alpha x(t)=\delta…
Quasi steady state assumptions are often used to simplify complex systems of ordinary differential equations in modelling of biochemical processes. The simplified system is designed to have the same qualitative properties as the original…
We study a discrete time queueing system where deterministic arrivals have i.i.d. exponential delays $\xi_{i}$. The standard deviation $\sigma$ of the delay is finite, but its value is much larger than the deterministic unit service time.…
We propose a collocation method based on multivariate polynomial splines over triangulation or tetrahedralization for the numerical solution of partial differential equations. We start with a detailed explanation of the method for the…
Time delays are ubiquitous in industry, and they must be accounted for when designing control strategies. However, numerical optimal control (NOC) of delay differential equations (DDEs) is challenging because it requires specialized…
We present a delay-compensating control method that transforms exponentially stabilizing controllers for an undelayed system into a sample-based predictive controller with numerical integration. Our method handles both first-order and…