Related papers: Operator splitting for dissipative delay equations

Pseudospectral approximation reduces DDE (delay differential equations) to ODE (ordinary differential equations). Next one can use ODE tools to perform a numerical bifurcation analysis. By way of an example we show that this yields an…

We propose a splitting approach to solve the second-order Hamilton--Jacobi equation, reducing it to a heat step and a purely first-order step. The latter is implemented using a gradient value policy iteration algorithm, enabling efficient…

An operator C on a Hilbert space H dilates to an operator T on a Hilbert space K if there is an isometry V from H to K such that C=V^*TV. A main result of this paper is, for a positive integer d, the simultaneous dilation, up to a sharp…

A first order differential equation with a periodic operator coefficient acting in a pair of Hilbert spaces is considered. This setting models both elliptic equations with periodic coefficients in a cylinder and parabolic equations with…

Basing on the constraint equalities which arise from the algebra of the collinear conformal group and the conformal operator product expansion, we predict the solutions of the leading order evolution equations for the non-forward…

The solvability of a delay differential equation arising in the construction of quadratic cost functionals, i.e. Lyapunov functionals, for a linear time-delay system with a constant and a distributed delay is investigated. We present a…

Using the theory of evolutionary equations, we consider abstract differential equations including non-local integral operators. After providing a condition for the well-posedness of the addressed equation we consider a numerical method of…

We first strictly expressed the basic notions and research methods of abstract operators, which systematically expounded the main results of abstract operator theory. By combining abstract operators with the Laplace transform, we can easily…

We give an operator theoretic approach to the constructions of multiresolutions as they are used in a number of basis constructions with wavelets, and in Hilbert spaces on fractals. Our approach starts with the following version of the…

In this paper we use some basic facts from the theory of (matrix) Lie groups and algebras to show that many of the classical matrix splittings used to construct stationary iterative methods and preconditioniers for Krylov subspace methods…

We develop a complete theory of non-formal deformation quantization on the cotangent bundle of a weakly exponential Lie group. An appropriate integral formula for the star-product is introduced together with a suitable space of functions on…

We develop the concept of operators in Hilbert spaces which are similar to their adjoints via antiunitary operators, the latter being not necessarily involutive. We discuss extension theory, refined polar and singular-value decompositions,…

Compartmental ordinary differential equation (ODE) models are used extensively in mathematical biology. When transit between compartments occurs at a constant rate, the well-known linear chain trick can be used to show that the ODE model is…

We study the symmetry reduction of nonlinear partial differential equations which are used for describing diffusion processes in nonhomogeneous medium. We find ansatzes reducing partial differential equations to systems of ordinary…

In this paper we use key elements of the Olver's approach to Hamiltonian evolution equations in partial derivatives and propose an algebraic construction appropriate for Hamiltonian evolution systems with constraints.

This note introduces a special class of tuples of bounded operators on a Hilbert space. It is called the Agler Young class. Major results about this class include a Wold decomposition and a dilation theorem. The structure of the dilation is…

Iterative solution of QED evolution equations for non-singlet electron structure functions is considered. Analytical expressions in the fourth and fifth orders are presented in terms of splitting functions. Relation to the existing…

In this paper we explore a numerical scheme for a nonlinear fourth order system of partial differential algebraic equations that describes the dynamics of slender inextensible elastica as they arise in the technical textile industry.…

Explicit coupling property and gradient estimates are investigated for the linear evolution equations on Hilbert spaces driven by an additive cylindrical L\'evy process. The results are efficiently applied to establish the exponential…

In this paper we consider various splitting schemes for unsteady problems containing the grad-div operator. The fully implicit discretization of such problems would yield at each time step a linear problem that couples all components of the…