Calculation schemes for numerical solution of elliptic boundary-value problems for Schrödinger-type equations based on Kantorovich method that reduces the initial problem to a set of boundary-value problems for a system of ordinary second-order differential equations are presented. The reduced boundaryvalue problems are discretized using the high-accuracy finite element method and implemented i...

Free high-frequency longitudinal vibrations of an inhomogeneous nanosized rod are studied on the basis nonlocal theory elasticity. The upper part spectrum with wavelength comparable to internal characteristic dimension a nanorod is examined. An equations in integral form Helmholtz kernel, incorporating both local and phases, used as constitutive one. original integro-differential equation reduc...

In the paper, we analyze the L norm error estimate of lower order finite element methods for the fourth order problem. We prove that the best error estimate in the L norm of the finite element solution is of second order, which can not be improved generally. The main ingredients are the saturation condition established for these elements and an identity for the error in the energy norm of the f...

We present and implement a fourth-order projective dependency parsing algorithm that effectively utilizes both “grand-sibling” style and “tri-sibling” style interactions of third-order and “grand-tri-sibling” style interactions of forth-order factored parts for performance enhancement. This algorithm requires O(n5) time and O(n4) space. We implement and evaluate the parser on two languages—Engl...

In this article, we study a class of nonlinear singular boundaryvalue problems. We show the existence of positive weak solutions by using variational methods.

We develop a constraint algorithm for degenerate time-dependent Lagrangians of second order and solve the so-called fourth order diierential equation problem. The study is inspired in the Gotay and Nester constraint algorithm and the notion of intermediate spaces introduced by Grr acia, Pons and Romm an-Roy.