In this paper, we present a computational method for solving boundary integral equations with loga-rithmic singular kernels which occur as reformulations of a boundary value problem for the Laplacian equation. Themethod is based on the use of the Galerkin method with CAS wavelets constructed on the unit interval as basis.This approach utilizes the non-uniform Gauss-Legendre quadrature rule for ...

A finite element numerical method is investigated for fractional order elliptic boundary value problems with homogeneous Dirichlet type boundary conditions. It is pointed out that an appropriate stiffness matrix can be obtained by taking the prescribed fractional power of the stiffness matrix corresponding to the non-fractional elliptic operators. It is proved that this approach, which is also ...

This paper examines and develops matrix methods to approximate the eigenvalues of a fourth order Sturm-Liouville problem subjected to a kind of fixed boundary conditions, furthermore, it extends the matrix methods for a kind of general boundary conditions. The idea of the methods comes from finite difference and Numerov’s method as well as boundary value methods for second order regular Sturm-L...

For a system of M coupled Schrödinger equations, the relationship is found between the vector-valued norming constants and M + 1 spectra corresponding to the same potential matrix but different boundary conditions. Under a special choice of particular boundary conditions, this equation for norming vectors has a unique solution. The double set of norming vectors and associated spectrum of one of...

For a system of coupled Schrödinger equations, the relationship is found between the vector-valued norming constants and M + 1 spectra of the M-channel Sturm-Liouville operator with the same potential matrix but different boundary conditions. Under a special choice of particular boundary conditions, this equation for norming vectors has a unique solution. The norming vectors derived from M + 1 ...

We consider mixed boundary value problems in Physical Geodesy and study possibilities in order to transform them into a system of integral equations over the boundary of the domain. The system of integral equations can be solved numerically, by, e.g. boundary element methods, provided that (a) the mixed boundary value problem is uniquely solvable, (b) the system of integral equations is equival...

1. Solution of a two-point boundary value problem. We consider a linear dynamical system ˙ x = Ax, with x(t) ∈ R n. There is an n-dimensional subspace of solutions of this equation, so to single out one of the trajectories we can impose, roughly speaking, n equations. In the most common situation, we specify x(0) = x 0 , in which case the unique solution is x(t) = e tA x 0. This is called an in...

In this paper, classical and enriched finite element formulations to impose Bloch-periodic boundary conditions are proposed. Bloch-periodic boundary conditions arise in the description of wave-like phenomena in periodic media. We consider the quantum-mechanical problem in a crystalline solid, and derive the weak formulation and matrix equations for the Schrödinger and Poisson equations in a par...