Consider integration over the unit sphere in £ ¥ ¤ , especially when the integrand has singular behaviour in a polar region. In an earlier paper , a numerical integration method was proposed that uses a transformation that leads to an integration problem over the unit sphere with an integrand that is much smoother in the polar regions of the sphere. The… (More)
This paper describes an algorithm for the solution of a system of nonlinear equations F(X)-O, where 0 = (0. .. .. 0) ~ R", and F is a gwen continuous transformation of n-dimensional simplex S into R"(n >_ 2) The program is based on computation of the topological degree ((leg) of a mapping and a slmplex-b~sectlon scheme. The algorithm is primarily useful for… (More)
Contents Abstract Sinc approximation methods excel for problems whose solutions may have singularities, or innnite domains, or boundary layers. This article summarizes results obtained to date, on Sinc numerical methods of computation. Sinc methods provide procedures for function approximation over bounded or unbounded regions, encompassing interpolation,… (More)
In this paper we derive a Sinc procedure for the construction of a conformal map, f , of a simply connected domain, or Riemann surface B in the complex plane to the unit disc U. The construction is based on the solution of a boundary integral equation which always has a unique solution. We assume that @B, the boundary of B, consists of a nite number of… (More)
A convergence and error analysis is given for a Nystrr om method on a graded mesh based on sinc quadrature for an integral equation of the second kind with a Mellin type singularity. An application to the double-layer integral equation for planar domains with corners is described.