Related papers: On Differential-Algebraic Equations in Infinite Di…
Finite-time linear-quadratic control of partial differential-algebraic equations (PDAEs) is considered. The discussion is restricted to those that are radial with index $0$; this corresponds to a nilpotency degree of 1. We establish the…
Two combined methods for computing solutions of time-varying semilinear differential-algebraic equations (descriptor systems) are obtained. When constructing the methods, time-varying spectral projectors which can be found numerically are…
A characteristic feature of differential-algebraic equations is that one needs to find derivatives of some of their equations with respect to time, as part of so called index reduction or regularisation, to prepare them for numerical…
The main subject of the paper is the so-called Discrete Painlev\'e-1 Equation (DP1). Solutions of the DP1 are classified under criterion of their behavior while argument tends to infinity. The appropriate theorems of existence are proved.
Probabilistic solvers for ordinary differential equations (ODEs) have emerged as an efficient framework for uncertainty quantification and inference on dynamical systems. In this work, we explain the mathematical assumptions and detailed…
We discuss ordinary differential equations with delay and memory terms in Hilbert spaces. By introducing a time derivative as a normal operator in an appropriate Hilbert space, we develop a new approach to a solution theory covering…
Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…
We apply topological methods to obtain global continuation results for harmonic solutions of some periodically perturbed ordinary differential equations on a $k$-dimensional differentiable manifold $M \subseteq \mathbb{R}^m$. We assume that…
We study the stability of general $n$-dimensional nonautonomous linear differential equations with infinite delays. Delay independent criteria, as well as criteria depending on the size of some finite delays are established. In the first…
The set of linear, differential operators preserving the vector space of couples of polynomials of degrees n and n-2 in one real variable leads to an abstract associative graded algebra A(2). The irreducible, finite dimensional…
We study the asymptotic stability of a dissipative evolution in a Hilbert space subject to intermittent damping. We observe that, even if the intermittence satisfies a persistent excitation condition, if the Hilbert space is…
A previous article was devoted to an analysis of the symmetry properties of a class of first-order delay ordinary differential systems (DODSs). Here we concentrate on linear DODSs. They have infinite-dimensional Lie point symmetry groups…
We present a Hilbert space perspective to homogenization of standard linear evolutionary boundary value problems in mathematical physics and provide a unified treatment for (non-)periodic homogenization problems in thermodynamics,…
This work establishes a rigorous connection between stability properties of discrete-time algorithms (DTAs) and corresponding continuous-time dynamical systems derived through $ O(s^r) $-resolution ordinary differential equations (ODEs). We…
We analyze the spectral properties and peculiar behavior of solutions of a damped wave equation on a finite interval with a singular damping of the form $\alpha/x$, $\alpha>0$. We establish the exponential stability of the semigroup for all…
A stochastic differential equation with coefficients defined in a scale of Hilbert spaces is considered. The existence and uniqueness of finite time solutions is proved by an extension of the Ovsyannikov method. This result is applied to a…
We establish a consistency result by comparing two independent notions of generalised solutions to a large class of linear hyperbolic first order PDE systems with constant coefficients, showing that they eventually coincide. The first is…
Welcome to a beautiful subject in scientific computing: numerical solution of ordinary differential equations (ODEs) with initial conditions.
The numerical solution of differential equations can be formulated as an inference problem to which formal statistical approaches can be applied. However, nonlinear partial differential equations (PDEs) pose substantial challenges from an…
In this paper, we consider a variational formulation for the Dirichlet problem of the wave equation with zero boundary and initial conditions, where we use integration by parts in space and time. To prove unique solvability in a subspace of…