An a posteriori error estimator is presented for the boundary element method in a general framework. It is obtained by solving local residual problems for which a local concept is introduced to accommodate the fact that integral operators are nonlocal operators. The estimator is shown to have an upper and a lower bound by the constant multiples of the exact error in the energy norm for Symm’s a...

in this paper, we use a combination of legendre and block-pulse functionson the interval [0; 1] to solve the nonlinear integral equation of the second kind.the nonlinear part of the integral equation is approximated by hybrid legen-dre block-pulse functions, and the nonlinear integral equation is reduced to asystem of nonlinear equations. we give some numerical examples. to showapplicability of...

A mode III crack problem in a functionally graded material (FGM) modeled by anisotropic strain gradient elasticity theory is solved by the integral equation method. The gradient elasticity theory has two material characteristic lengths ` and `′, which are responsible for volumetric and surface strain-gradient terms, respectively. The governing differential equation of the problem is derived ass...

urysohn integral equation is one of the most applicable topics in both pure and applied mathematics. the main objective of this paper is to solve the urysohn type fredholm integral equation. to do this, we approximate the solution of the problem by substituting a suitable truncated series of the well known legendre polynomials instead of the known function. after discretization of the problem o...

The article is devoted to the issue of construction an optimal with respect order passive algorithms for evaluating Cauchy and Hilbert singular hypersingular integrals oscillating kernels. We propose a method estimating lower bound errors quadrature formulas integral evaluation. Quadrature were constructed implementation obtained estimates. estimated This based on using similar results integrals.