The main focus of the meeting was on boundary value problems for general differential operators L = −divA∇. Here A is an elliptic matrix with variable coefficients, given by complex-valued bounded and measurable functions. Such operators arise naturally in many problems of pure mathematics as well as in numerous applications. In particular, they describe a wide array of physical phenomena in ro...

Exact and approximate analytical solutions of linear and nonlinear singular two-point boundary value problems (BVPs) are obtained for the first time by the Legendre operational matrix of differentiation. Different from other numerical techniques, shifted Legendre polynomials and their properties are employed for deriving a general procedure for forming this matrix. The accuracy of the technique...

This paper considers the hp-finite element discretization of an elliptic boundary value problem using tetrahedral elements. The discretization uses a polynomial basis in which the number of nonzero entries per row is bounded independently of the polynomial degree. The authors present an algorithm which computes the nonzero entries of the stiffness matrix in optimal complexity. The algorithm is ...

We consider an inverse problem of determining a coefficient matrix and an initial value for a first order hyperbolic system. Assuming that the boundary values over a time interval are known, we characterize coefficient matrices and initial values, and prove the uniqueness of some components of the matrix function. The proof is based on a transformation formula and the spectral properties of the...

We study the generalized supersymmetric t − J model with Kondo impurities in the boundaries. We first construct the higher spin operator K-matrix for the XXZ Heisenberg chain. Setting the boundary parameter to be a special value, we find a higher spin reflecting K-matrix for the supersymmetric t− J model. By using the Quantum Inverse Scattering Method, we obtain the eigenvalue and the correspon...

We study the generalized supersymmetric t − J model with Kondo impurities in the boundaries. We first construct the higher spin operator K-matrix for the XXZ Heisenberg chain. Setting the boundary parameter to be a special value, we find a higher spin reflecting K-matrix for the supersymmetric t− J model. By using the Quantum Inverse Scattering Method, we obtain the eigenvalue and the correspon...

In this paper, we investigate some properties of eigenvalues and eigenfunctions of boundary value problems with separated boundary conditions. Also, we obtain formal series solutions for some partial differential equations associated with the second order differential equation, and study necessary and sufficient conditions for the negative and positive eigenvalues of the boundary value problem....

In this article we have proposed an accurate finite difference method for approximate numerical solution of second order boundary value problem with Dirichlet boundary conditions. There are numerous numerical methods for solving these boundary value problems. Some these methods are more efficient and accurate than others with some advantages and disadvantages. The results in experiment on model...

A sequence of least squares problems of the form miny kG 1=2 (A T y ? h)k2 where G is an n n positive deenite diagonal weight matrix, and A an m n (m < n) sparse matrix with some dense columns; has many applications in linear programming, electrical networks, elliptic boundary value problems, and structural analysis. We discuss a technique for forming low-rank correction pre-conditioners for su...

We analyse an initial-boundary value problem for the mKdV equation on a finite interval by expressing the solution in terms of the solution of an associated matrix Riemann-Hilbert problem in the complex k-plane. This Riemann-Hilbert problem has explicit (x, t)-dependence and it involves certain functions of k referred to as “spectral functions”. Some of these functions are defined in terms of t...