Singular integral equation that has enormous applications in applied problems including fluid mechanics, biomechanics, electromagnetic theory and chemistry applications such as heat conduction, crystal growth and electrochemistry. An integral equation is called a singular integral equation if one or both limits of integration become infinite, or if the kernel of the equation becomes infinite at...

Let Σ be a weighted homogeneous (singular) subvariety of C . The main objective of this paper is to present a class of explicit integral formulae for solving the ∂-equation ω = ∂λ on the regular part of Σ, where ω is a ∂-closed (0, q)-form with compact support and degree q ≥ 1. Particular cases of these formulae yield L-bounded solution operators for 1 ≤ p ≤ ∞ if Σ is a homogeneous and pure dim...

We consider a fully discrete qualocation method for Symm's integral equation. The method is that of Sloan and Burn 14], for which a complete analysis is available in the case of smooth curves. The convergence for smooth curves can be improved by a subtraction of singularity (Jeon and Kimn 10]). In this paper we extend these results for smooth boundaries to polygonal boundaries. The analysis use...

We study the multiplicative Schwarz method for the p-version Galerkin boundary element method for a hypersingular and a weakly singular integral equation of the rst kind and for the h-version for a hypersingular integral equation of the rst kind. We prove that the rate of convergence of the multiplicative Schwarz operator is strictly less than 1 for the h-version for both two level and multilev...

A high order accurate and fast algorithm is constructed for 2D stress problems on multiply connected finite domains. The algorithm is based on a Fredholm integral equation of the second kind with non-singular operators. The unknown quantity is the limit of an analytic function. On polygonal domains there is a trade-off between stability and rate of convergence. A moderate amount of precomputati...

A two-dimensional nonlinear aerodynamics representation analysis is proposed for the investigation of inviscid flowfields of unsteady airfoils. Such problems are reduced to the solution of a nonlinear multidimensional singular integral equation as the source and vortex strength distributions are dependent on the history of these distributions on the NACA airfoil surface. A turbulent boundary la...

By a quasi-permutation matrix, we mean a square non-singular matrix over the complex field with non-negative integral trace....

In this work we consider the numerical computation of eigenpairs of a matrix derived from integral operators. The matrix is associated to a radiative transfer problem in stellar atmospheres that is formulated by means of a weakly singular Fredholm integral equation defined on a Banach space. We examine direct and iterative parallel strategies for the eigensolution phase, using state-of-the-art ...

In this work we are concerned with the numerical solution of a nonlinear weakly singular Volterra integral equation with a nonsmooth solution. We investigate the application of product integration methods and a detailed analysis of the Trapezoidal method is given. In order to improve the numerical results we consider extrapolation procedures and collocation methods based on graded meshes. Sever...