‎in this paper‎, ‎an approach based on statistical spline model (ssm) and collocation method is proposed to solve volterra-fredholm integral equations‎. ‎the set of collocation nodes is chosen so that the points yield minimal error in the nodal polynomials‎. ‎under some standard assumptions‎, ‎we establish the convergence property of this approach‎. ‎numerical results on some problems are given...

In this paper we analyze a Galerkin procedure, based on a combination of finite and spectral elements, for approximating a time-harmonic acoustic wave scattered by a bounded inhomogeneity. The finite element method used to approximate the near field in the region of inhomogeneity is coupled with a nonlocal boundary condition, which consists in a linear integral equation. This integral equation ...

In this work, variational integrators of higher order for dynamical systems with holonomic constraints are constructed and analyzed. The construction is based on approximating the configuration and theLagrangemultiplier via different polynomials. The splitting of the augmented Lagrangian in two parts enables the use of different quadrature formulas to approximate the integral of each part. Cond...

For the unit sphere embedded in a Euclidean space, we obtain quadrature formulas that are exact for spherical harmonics of a fixed order, have nonnegative weights, and are based on function values at scattered points (sites). The number of scattered sites required is comparable to the dimension of the space for which the quadrature formula is required to be exact. As a part of the proof, we der...

In this paper we solve the problem about optimal interval quadrature formula for the class WrF of differentiable periodic functions with rearrangement invariant set F of their derivatives of order r. We prove that the formula with equal coefficients and n node intervals having equidistant midpoints is optimal for considering classes. To this end a sharp inequality for antiderivatives of rearran...

Similar as in the classical case of polynomials, as is known, paraorthogonal rational functions on the unit circle can be used to obtain quadrature formulas of Szegő-type to approximate some integrals. In the present paper we carry out a thorough discussion of the existence of such rational functions in terms of the underlying Borel measure on the unit circle

in this paper, we will present a review of the multistep collocation method for delay volterra integral equations (dvies) from [1] and then, we study the superconvergence analysis of the multistep collocation method for dvies. some numerical examples are given to confirm our theoretical results.

An algorithm is described for the efficient numerical solution of singular two-point boundary value problems. The algorithm is based on collocation at Gauss points, is applied directly to second order equations and uses a transformation of the independent variable to obtain extra smoothness if needed. Numerical comparisons between a code based on this approach and codes based on other options w...

Newton-HSS methods, that are variants of inexact Newton methods different from Newton-Krylov methods, have been shown to be competitive methods for solving large sparse systems of nonlinear equations with positive definite Jacobian matrices [Bai and Guo, 2010]. In that paper, only local convergence was proved. In this paper, we prove a Kantorovich-type semilocal convergence. Then we introduce N...