The aim of this paper is the investigation of the error which results from the method of approximate approximations applied to functions defined on compact intervals, only. This method, which is based on an approximate partition of unity, was introduced by V. Maz’ya in 1991 and has mainly been used for functions defined on the whole space up to now. For the treatment of differential equations a...

In this paper, a highly accurate parallel difference scheme for the fourth-order diffusion equation is studied. Based on a group of new Saul’yev type asymmetric difference schemes, a high-order, unconditionally stable and parallel alternating group explicit scheme is derived. The scheme is fourth-order truncation error in space, which is much more accurate than the known methods. Numerical expe...

Recently, MOESP-type closed-loop subspace model identification (CL-MOESP) has been proposed by the authors and its effectiveness has been demonstrated via both numerical simulations and real-life systems, e.g., a cart-inverted pendulum system. However, asymptotic properties of CLMOESP has not yet been studied. The purpose of this paper is to clarify the asymptotic properties of CL-MOESP from th...

The Gegenbauer reconstruction method effectively eliminates the Gibbs phenomenon and restores exponential accuracy to the approximations of piecewise smooth functions. Recent investigations show that its success depends upon choosing parameters in such a way that the regularization and the truncation error estimates are equally considered. This paper shows that the underlying analyticity of the...

We present an isogeometric analysis of time-harmonic exterior acoustic problems. The infinite space is truncated by a fictitious boundary and (simple) absorbing boundary conditions are applied. The truncation error is included in the exact solution so that the reported error is an indicator of the performance of the isogeometric analysis, in particular of the related pollution error. Numerical ...

A verified integration algorithm is proposed for calculating s-dimensional integrals over a finite domain using numerical computations. To construct an efficient verified numerical integrator, the truncation error and the rounding error need to be considered. It has been known that interval arithmetic is one of the most efficient methods of evaluating the rounding error. However, it is much slo...