Estimation of error in approximate numerical integration near a simple pole using Chebyshev points

NUMERICAL SOLUTION OF INTEGRO-DIFFERENTIAL EQUATION BY USING CHEBYSHEV WAVELET OPERATIONAL MATRIX OF INTEGRATION

In this paper, we propose a method to approximate the solution of a linear Fredholm integro-differential equation by using the Chebyshev wavelet of the first kind as basis. For this purpose, we introduce the first Chebyshev operational matrix of integration. Chebyshev wavelet approximating method is then utilized to reduce the integro-differential equation to a system of algebraic equations. Il...

Error bounds for approximation in Chebyshev points

This paper improves error bounds for Gauss, Clenshaw-Curtis and Fejér’s first quadrature by using new error estimates for polynomial interpolation in Chebyshev points. We also derive convergence rates of Chebyshev interpolation polynomials of the first and second kind for numerical evaluation of highly oscillatory integrals. Preliminary numerical results show that the improved error bounds are ...

Near Pole Polar Diagram of Points and its Duality with Applications

In this paper we propose a new approach to plane partitioning with similar features to those of Polar Diagram, but we assume that the pole is close to the sites. The result is a new tessellation of the plane in regions called Near Pole Polar Diagram NPPD. Here we define the (NPPD) of points, the dual and the Contracted dual of it, present an optimal algorithms to draw them and discuss the appli...

A Numerical Integration Method by Using Generalized Series of Functions

Near-Circularity of the Error Curve In Complex Chebyshev Approximation

Let f(z) be analytic on the unit disk, and let p*(z) be the best (Chebyshev) polynomial approximation to f(z) on the disk of degree at most n. It is observed that in typical problems the “error curve,” the image of the unit circle under (f p*)(z), often approximates to a startling degree a perfect circle with winding number n + 1. This phenomenon is approached by consideration of related proble...