Using some recent results on subperiodic trigonometric interpolation and quadrature, and the theory of admissible meshes for multivariate polynomial approximation, we study product Gaussian quadrature, hyperinterpolation and interpolation on some regions of Sd, d ≥ 2. Such regions include caps, zones, slices and more generally spherical rectangles defined by longitudes and (co)latitudes (geogra...

Neural Networks have been widely used to solve Partial Differential Equations. These methods require approximate definite integrals using quadrature rules. Here, we illustrate via 1D numerical examples the problems that may arise in these applications and propose different alternatives overcome them, namely: Monte Carlo methods, adaptive integration, polynomial approximations of Network output,...

Abstract In this work, in order to obtain higher-order schemes for solving forward backward stochastic differential equations, we propose a new multi-step scheme by adopting the high-order method Zhao et al. (SIAM J. Sci. Comput., 36(4): A1731-A1751, 2014) with combination technique. Two reference ordinary equations containing conditional expectations and their derivatives are derived from comp...

Abstract. It was shown by P. J. Davis that the Newton-Cotes quadrature formula is convergent if the integrand is an analytic function that is regular in a sufficiently large region of the complex plane containing the interval of integration. In the present paper, a bound on the error of the Newton-Cotes quadrature formula for analytic functions is derived. Also the bounds on the Legendre polyno...

in this paper, eringen’s nonlocal elasticity and timoshenko beam theories are implemented to analyze the bending vibration for non-uniform nano-beams.  the governing equations and the boundary conditions are derived using hamilton’s principle. a generalized differential quadrature method (gdqm) is utilized for solving the governing equations of non-uniform timoshenko nano-beam for pinned-pinned...

In this paper, a numerical algorithm using a coupled Galerkin-Differential Quadrature (DQ) method is proposed for the solution of dam-reservoir interaction problem. The governing differential equation of motion of the dam structure is discretized by the Galerkin method and the DQM is used to discretize the fluid domain. The resulting systems of ordinary differential equations are then solved by...

In this article, we study the numerical solution of the one dimensional nonlinear sineGordon by using the modified cubic B-spline differential quadrature method (MCB-DQM). The scheme is a combination of a modified cubic B-spline basis function and the differential quadrature method. The modified cubic B-spline is used as a basis function in the differential quadrature method to compute the weig...

Let D be a real function such that D(z) is analytic and D(z) ± 0 for \z\ < 1. Furthermore, put W(x) = \J\ x2\D(e'v)\2 , x = costp , tp e [0, 71 ], and denote by pn(', rV) the polynomial which is orthogonal on [-1, +1] to Pn_[ (P„_! denotes the set of polynomials of degree at most n 1 ) with respect to W . In this paper it is shown that for each sufficiently large n the polynomial En+X(-, W) (ca...

‎in this paper, we formulate the fourth order sturm-liouville problem (fslp) as a lie group matrix differential equation. by solving this ma- trix differential equation by lie group magnus expansion, we compute the eigenvalues of the fslp. the magnus expansion is an infinite series of multiple integrals of lie brackets. the approximation is, in fact, the truncation of magnus expansion and a gauss...

We introduce an interpolation process based on some of the zeros of the mth generalized Freud polynomial. Convergence results and error estimates are given. In particular we show that, in some important function spaces, the interpolating polynomial behaves like the best approximation. Moreover the stability and the convergence of some quadrature rules are proved.