Abstract This paper studies the problem of construction of optimal quadrature formulas in the sense of Sard in the space ( ) 2 (0,1) m L . In this paper the quadrature sum consists of values of the integrand and its first derivative at nodes. The coefficients of optimal quadrature formulas are found and the norm of the optimal error functional is calculated for arbitrary natural number 1 N m ≥ ...

An important step in simulation via isogeometric analysis (IGA) is the assembly step, where the coefficients of the final linear system are generated. Typically, these coefficients are integrals of products of shape functions and their derivatives. Similarly to the finite element analysis (FEA), the standard choice for integral evaluation in IGA is Gaussian quadrature. Recent developments propo...

Non-parametric modeling is a method which relies heavily on data and motivated by the smoothness properties in estimating a function which involves spline and non-spline approaches. Spline approach consists of regression spline and smoothing spline. Regression spline with Bayesian approach is considered in the first step of a two-step method in estimating the structural parameters for stochasti...

A general framework for proving an order of convergence for set-valued Runge Kutta methods is given in the case of linear differential inclusions, if the attainable set at a given time should be approximated. The set-valued method is interpreted as a (set-valued) quadrature method with disturbed values for the fundamental solution at the nodes of the quadrature method. If the precision of the q...

The use of quadrature RF magnetic fields has been demonstrated to be an efficient method to reduce transmit power and to increase the signal-to-noise (SNR) in magnetic resonance (MR) imaging. The goal of this project was to develop a new method using the common-mode and differential-mode (CMDM) technique for compact, planar, distributed-element quadrature transmit/receive resonators for MR sign...

In this paper, we use a numerical method involving collocation method with third B-splines as basis functions for solving a class of singular initial value problems (IVPs) of Lane--Emden type equation. The original differential equation is modified at the point of singularity. The modified problem is then treated by using B-spline approximation. In the case of non-linear problems, we first line...

This paper extends the application of Differential Quadrature Method (DQM) for finding the numerical solution of general singularly perturbed two point boundary value problems with a boundary layer at right end point or both end point or at an internal point. The Differential Quadrature Method is an efficient descritization technique in solving initial and /or boundary value problems accurately...

plates and shells are the significant structural components for many engineering and industrial applications. in this study, free vibration analysis of annular plates is investigated. for this, two different numerical methods such as differential quadrature and discrete singular convolution methods have been performed for numerical simulations. frequency values have been obtained via these two ...