Oscillatory integrals over fan-shaped regions widely exist in scattering analysis, and this paper proposes a new rapid calculation routine for them. In the routine, the concerned bivariate scattering oscillatory integral is reduced to the calculation of two univariate oscillatory integrals. One is calculated with the improved Levin quadrature method, and another is transformed to a non-oscillat...

A hypersingular integral can be regularized by replacing the whole integrand by a forward difference quotient of 2nd order. If the density function is nearly singular, then Gauss quadrature formulas associated with a suitable modification of the Chebyshev weight function allow to obtain great precision with few nodes. However, in most cases, the own nature of this procedure makes unpredictable ...

We study the numerical solutions to semi-infinite-domain two-point boundary value problems and initial value problems. A smooth, strictly monotonic transformation is used to map the semiinfinite domain x ∈ 0,∞ onto a half-open interval t ∈ −1, 1 . The resulting finite-domain twopoint boundary value problem is transcribed to a system of algebraic equations using ChebyshevGauss CG collocation, wh...

In this paper, three numerical solutions for the Kortewegde Vries Burgers’ (KdVB) equation are presented. Two of these methods are based on cardinal Chebyshev basis function with Galerkin method. Gauss-quadrature formula and El-gendi method are used to convert the problem into system of ordinary differential equations. In the third proposed method, the cardinal Legendre basis function with Gale...

this paper gives an ecient numerical method for solving the nonlinear systemof volterra-fredholm integral equations. a legendre-spectral method based onthe legendre integration gauss points and lagrange interpolation is proposedto convert the nonlinear integral equations to a nonlinear system of equationswhere the solution leads to the values of unknown functions at collocationpoints.

one of the simplest numerical integration method which provides a large saving in computational efforts, is the well known one-point Gauss quadrature which is widely used for 4 nodes quadrilateral elements. On the other hand, the biggest disadvantage to one-point integration is the need to control the zero energy modes, called hourglassing modes, which arise. The efficiency of four different an...

The Gauss map of a smooth doubly{curved surface characterizes the range of variation of the surface normal as an area on the unit sphere. An algorithm to approximate the Gauss map boundary to any desired accuracy is presented, in the context of a tensor{product polynomial surface patch, r(u;v) for (u; v) 2 0; 1 ] 0; 1 ]. Boundary segments of the Gauss map correspond to variations of the normal ...

An O(N(logN)2/ loglogN) algorithm for computing the discrete Legendre transform and its inverse is described. The algorithm combines a recently developed fast transform for converting between Legendre and Chebyshev coefficients with a Taylor series expansion for Chebyshev polynomials about equallyspaced points in the frequency domain. Both components are based on the FFT, and as an intermediate...

This article considers the extension of V. A. Markov’s theorem for polynomial derivatives to polynomials with unit bound on the closed unit ball of any real normed linear space. We show that this extension is equivalent to an inequality for certain directional derivatives of polynomials in two variables that have unit bound on the Chebyshev nodes. We obtain a sharpening of the Markov inequality...