A Fully-Discrete Trigonometric Collocation Method

Fully Discrete Collocation Method for Weakly Singular Integral Equations

Abstract. To find the approximate solutions of a weakly singular integral equation by the collocation method it is necessary to solve linear systems whose coefficients are expressed as integrals. These integrals cannot usually be computed exactly. We get the fully discrete collocation method when we approximate the integrals by quadrature formulas on nonuniform grid. In this paper an appropriat...

A discrete trigonometric interpolation method

Interpolation theory is a necessary and crucial tools for many applied engineering sciences. In this paper, we propose a new kind of 2-period interpolation of functions with period 2 at the nodes x k = x k;n = k=n; (k = 0; 1; ; 2n ? 1). We nd out the necessary and suucient conditions for regularity of this new interpolation problem. Moreover, a closed form expression for the interpolation polyn...

A Fully Discrete Collocation Method for High Frequency Scattering by Convex Polygons

We consider the numerical solution of the problem of time-harmonic acoustic scattering in two dimensions by a sound soft convex polygon. Standard boundary or finite element methods with piecewise polynomial approximation spaces have a computational cost that grows at least linearly with respect to the frequency of the incident wave. By including in the approximation space the products of plane ...

Discrete Collocation Method for Solving Fredholm Volterra Intergro-Differential Equations

A Discrete Collocation Method for Boundary Integral Equations

We propose a discrete collocation method for the boundary integral equations which arise from solving Laplace's equation u = 0. The Laplace's equation is deened on connected regions D in R 3 with a smooth boundary S. The piecewise polynomial interpolation in the parametrization variables along with the collocation method is used, and a numerical integration scheme for collocation integrals is g...