the asymmetric problem of rocking rotation of a circular rigid disk embedded in a finite depth of a transversely isotropic half-space is analytically addressed. the rigid disk is assumed to be in frictionless contact with the elastic half-space. by virtue of appropriate green's functions, the mixed boundary value problem is written as a dual integral equation. employing further mathematica...

We study the condition number of the system matrices that appear in the Boundary Element Method when solving the Stokes equations at a two-dimensional domain. At the boundary of the domain we impose Dirichlet conditions or mixed conditions. We show that for certain critical boundary contours the underlying boundary integral equation is not solvable. As a consequence, the condition number of the...

In this paper we study boundary integral formulations of the interior and exterior Dirichlet problem for the bi{Laplacian in a plane domain with a piecewise smooth boundary having corner points. The mapping properties of single and double layer bihar-monic potentials, of the Calderon projections and the Poincar e-Steklov operators for such domains are analysed. We derive direct boundary integra...

An infinitely long hollow cylinder containing isotropic linear elastic material is considered under the effect of arbitrary boundary stress and thermal condition. The two-dimensional coupled thermoelastodynamic PDEs are specified based on equations of motion and energy equation, which are uncoupled using Nowacki potential functions. The Laplace integral transform and Bessel-Fourier series are u...

Radial basis functions are used to define approximate solutions to boundary integral equations on the unit sphere. These equations arise from the integral reformulation of the Laplace equation in the exterior of the sphere, with given Dirichlet or Neumann data, and a vanishing condition at infinity. Error estimates are proved. Numerical results supporting the theoretical results are presented.

The paper studies boundary integral operators of the bi{Laplacian on piecewise smooth curves with corners and describes their mapping properties in the trace spaces of variational solutions of the biharmonic equation. We formulate a direct integral equation method for solving mixed boundary value problems for the biharmonic equation on a nonsmooth plane domain, analyse the solvability of the co...

This paper studies a boundary value problem of nonlinear second-order q-difference equations with non-separated boundary conditions. As a first step, the given boundary value problem is converted to an equivalent integral operator equation by using the q-difference calculus. Then the existence and uniqueness of solutions of the problem is proved via the resulting integral operator equation by m...

By constructing an available integral operator and combining fixed point index theory with properties of Green’s function, this paper shows the existence of multiple positive solutions for a class of impulsive singular boundary value problems with integral boundary conditions. Our results extend some recent work in the literature on boundary value problems of ordinary differential equations. We...

in this paper, we will compare a homotopy perturbation algorithm and taylor series expansin method for a system of second kind fredholm integral equations. an application of he’s homotopy perturbation method is applied to solve the system of fredholm integral equations. taylor series expansin method reduce the system of integral equations to a linear system of ordinary differential equation.