On the half line 0; 1) we study rst order diierential operators of the form B 1 i d dx + Q(x); where B := B 1 0 0 ?B 2 ; B 1 ; B 2 2 M(n; C) are self{adjoint positive deenite matrices and Q : R + ! M(2n; C); R + := 0; 1); is a continuous self{adjoint oo{diagonal matrix function. We determine the self{adjoint boundary conditions for these operators. We prove that for each such boundary value pro...

We consider the efficient deterministic solution of elliptic boundary value problems with random diffusion matrix. Assuming random perturbations with known k moments, we derive, to leading order in the random perturbation’s amplitude, deterministic equations for k moments of the random solution. The solution’s k-th moment satisfies a k-fold tensor product boundary value problem on the k-fold pr...

Linear multistep methods are considered which have a stability region S and are D-stable on the whole boundary S c S of S. Error estimates are derived which hold uniformly for the class of initial value problems Y’ AY + B(t), t > 0, Y(0) Y with normal matrix A satisfying the spectral condition Sp(AtA) S At O time step, Sp(A) spectrum of A. Because of this property, the result can be applied to ...

We consider precondition of linear systems resulting from the finite volume element method (FVEM) for elliptic boundary value problems. With the help of the interpolation operator from a trial space to a test space and the operator induced by the FVEM bilinear form, we show that both wavelet preconditioners and multilevel preconditioners designed originally for the finite element method for the...

We consider linear boundary value problems for higher-order parameter-elliptic equations, where the data do not belong to classical trace spaces. employ a class of Sobolev spaces mixed smoothness that admits generalized with values in Besov negative order. prove unique solvability rough half-space and sufficiently smooth domains. As an application, we show operator related linearized Cahn–Hilli...

We survey some known results about generator property of operator matrices with diagonal or coupled domain. Further, we use basic properties of the convolution of operator-valued mappings in order to obtain stability results for such semigroups. 1. Operator matrices with diagonal domain While tackling abstract problems that are related to concrete initial–boundary value problems with dynamical ...

This contribution deals with the numerical solution of elliptic boundary value problems with unilateral boundary conditions using a fictitious domain method. Any fictitious domain formulation [2] extends the original problem defined in a domain ω to a new (fictitious) domain Ω with a simple geometry (e.g. a box) which contains ω. The main advantage consists in possibility to use a uniform mesh ...

Vargas et al. @Phys. Rev. E 53, 1954 ~1996!# presented a numerical matrix method to solve the onedimensional Schrödinger equation subject to Dirichlet boundary conditions. It is a well-known fact that the eigensolutions of such a confined system converge asymptotically to those of the corresponding unbounded problem as the boundary value increases. However, it is verified computationally that t...

In this work we analyze regular boundary value problems on a distance-regular graph associated with Schrödinger operators. These problems include the cases in which the boundary has two or one vertices. Moreover, we obtain the Green matrix for each regular problem. In each case, the Green matrices are given in terms of two families of orthogonal polynomials one of them corresponding with the di...