The efficiency of hierarchical matrices is based on the approximate evaluation of usual matrix operations. The introduced approximation error may, however, lead to a loss of important matrix properties. In this article we present a technique which preserves the positive definitness of a matrix independently of the approximation quality. The importance of this technique is illustrated by an elli...

We consider the open XXZ quantum spin chain with nondiagonal boundary terms. For bulk anisotropy value η = iπ p+1 , p = 1 , 2 , . . ., we propose an exact (p+1)-order functional relation for the transfer matrix, which implies Bethe-Ansatz-like equations for the corresponding eigenvalues. The key observation is that the fused spin2 transfer matrix can be expressed in terms of a lower-spin transf...

The macro{hybrid formulation based on domain decomposition is considered for elliptic boundary value problems with both symmetric positive deenite and indeenite operators. The problem is discretized by the mortar element method, which leads to a large{scale sparse linear system with a saddle{ point matrix. In the case of symmetric and positive deenite operators, a block diagonal preconditioner ...

Abstract. We report a new analytical method for solution of a wide class of second-order differential equations with eigenvalues replaced by arbitrary functions. This approach is based on the extension of the previously reported differential transfer matrix method with modified basis functions. Applications of the method to boundary value and initial value problems, as well as several examples ...

In this paper, we concerned with positive solutions for higher order m-point nonlinear fractional boundary value problems with integral boundary conditions. We establish the criteria for the existence of at least one, two and three positive solutions for higher order m-point nonlinear fractional boundary value problems with integral boundary conditions by using a result from the theory of fixed...

Fractional calculus has been used to model physical and engineering processes that are found to be best described by fractional diff<span style="font-family: NimbusRomNo...

in this paper, using the fixed point theory in cone metric spaces, we prove the existence of a unique solution to a first-order ordinary differential equation with periodic boundary conditions in banach spaces admitting the existence of a lower solution.

A new boundary-integral formulation is proposed to analyze the heat transfer in zoned three-dimensional geometries. The proposed formulation couples the boundary formula, the gradient of the boundary formula, and the exterior formula. An advantage of this formulation over the traditional methods is that any linear condition at the interface between subdomains may be incorporated into the formul...

‎in this paper‎, ‎we provide sufficient conditions for the existence of nonnegative solutions of a boundary value problem for a fractional order differential equation‎. ‎by applying kranoselskii`s fixed--point theorem in a cone‎, ‎first we prove the existence of solutions of an auxiliary bvp formulated by truncating the response function‎. ‎then the arzela--ascoli theorem is used to take $c^1$ ...