Automatic Resolution Control for the Finite Volume Method (FVM) shows signs of rapid development in recent years. The objective of the procedure is to obtain a numerical solution of prescribed accuracy with minimum eeort in terms of time and computational resources. It consists of two parts: an a-posteriori error estimate and an appropriate modii-cation of the spatial and temporal discretisatio...

A random vector X with given univariate marginals can be obtained by first applying the normal distribution function to each coordinate of a vector Z of correlated standard normals to produce a vector U of correlated uniforms over (0, 1) and then transforming each coordinate of U by the relevant inverse marginal. One approach to fitting requires, separately for each pair of coordinates of X, th...

Universal (pointwise uniform and time shifted) truncation error upper bounds are presented for the Whittaker–Kotel'nikov–Shannon (WKS) sampling restoration sum for Bernstein function classes B q π,d , q > 1, d ∈ N, when the decay rate of the sampled functions is unknown. The case of regular sampling is discussed. Extremal properties of related series of sinc functions are investigated.

Balanced truncation is the most commonly used model order reduction scheme in control engineering. This is due to its favorable properties of automatic stability preservation and the existence of a computable error bound, enabling the adaption of the reduced model order to a specified tolerance. It aims at minimizing the worst case error of the frequency response over the full infinite frequenc...

A Class of new methods based on a septic non-polynomial spline function for the numerical solution of problems in calculus of variations is presented. The local truncation errors and the methods of order 2th, 4th, 6th, 8th, 10th, and 12th, are obtained. The inverse of some band matrixes are obtained which are required in proving the convergence analysis of the presented method. Convergence anal...