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 ...

In this paper, a nonlinear Volterra-Fredholm integral equation of the first kind is solved by using the homotopy analysis method (HAM). In this case, the first kind integral equation can be reduced to the second kind integral equation which can be solved by HAM. The approximate solution of this equation is calculated in the form of a series which its components are computed easily. The accuracy...

In this paper, six error indicators obtained from dual boundary integral equations are used for local estimation, which is an essential ingredient for all adaptive mesh schemes in BEM. Computational experiments are carried out for the two-dimensional Laplace equation. The curves of all these six error estimators are in good agreement with the shape of the error curve. The results show that the ...

A Galerkin boundary integral procedure for evaluating the complete derivative, e.g., potential gradient or stress tensor, is presented. The expressions for these boundary derivatives involve hypersingular kernels, and the advantage of the Galerkin approach is that the integrals exist when a continuous surface interpolation is employed. As a consequence, nodal derivative values, at smooth surfac...

in this article, a transversely isotropic linear elastic half-space with depth wise isotropy axis of material containing a cylindrical cavity of finite length is considered to be under the effect of an arbitrary torsion force applied on the wall of the cavity. to this end, the equation of equilibrium has been written in a cylindrical coordinate system, by dividing the involved domain to two reg...

In this paper, we use the continuous Legendre wavelets on the interval [0,1] constructed by Razzaghi M. and Yousefi S. [6] to solve the linear second kind integral equations. We use quadrature formula for the calculation of the products of any functions, which are required in the approximation for the integral equations. Then we reduced the integral equation to the solution of linear algebraic ...

In this supplement to [14], we propose a new Calderón-type preconditioner for the weakly singular integral operator for −∆ on screens in R. We introduce a modified hypersingular operator, which is the exact inverse of the weakly singular operator on the unit disk. It forms the foundation for dual-mesh-based operator preconditioning. Applied to low-order boundary element Galerkin discretizations...

In this paper we present a treatment of hypersingular integral equations, which have relevant applications in many problems of wave dynamics, elasticity and fluid mechanics with mixed boundary conditions. The main goal of the present work is the development of an efficient direct numerical collocation method. The paper is completed with two examples taken from crack theory and acoustics: the st...

The importance of singular and hypersingular integral transforms, coming from their many applications, justifies some interest in their numerical approximation. The literature about the numerical evaluation of such integrals on bounded intervals is wide and quite satisfactory; instead only few papers deal with the numerical evaluation of such integral transforms on half-infinite intervals or on...