# convergence

## Identification of parameters of interval nonlinear models of static systems using multidimensional optimization

The article proposes an approach to parametric identification of interval nonlinear models of static systems based on the standard problem of minimizing the root mean square deviation between the values ​​of the modeled characteristics of the static object and the values ​​belonging to the experimental intervals.

## New development of homotopy analysis method for non-linear integro-differential equations with initial value problems

Homotopy analysis method (HAM) was proposed by Liao in 1992 in his PhD thesis for non-linear problems and was applied in many different problems of mathematical physics and engineering.  In this note, a new development of homotopy analysis method (ND-HAM) is demonstrated for non-linear integro-differential equation (NIDEs) with initial conditions.  Practical investigations revealed that ND-HAM leads an easy way how to find initial guess and it approaches the exact solution faster than the standard HAM, modified HAM (MHAM), new modified of HAM (mHAM) and more general method of HAM (q-HAM).

## Convergence and cross-media: discourse term logic paradigm

The paper identifies key interpretation of convergence; on the basis of their analysis are systematized and tendencies within the meaning of the term and its dynamics of social communication; cross-media understanding is proposed as the implementation process of media convergence trends. The author notes that the media industry is changing rapidly and facing the development and combination of different media formats.

## Finite element approximations in projection methods for solution of some Fredholm integral equation of the first kind

Approximation properties of B-splines and Lagrangian finite elements in Hilbert spaces of functions defined on surfaces in three-dimensional space are investigated.  The conditions for the convergence of Galerkin and collocation methods for solution of the Fredholm integral equation of the first kind for the simple layer potential that is equivalent to the Dirichlet problem for Laplace equation in $\mathbb{R}^3$ are established.  The estimation of the error of approximate solution of this problem, obtained by means of the potential theory methods, is determined.