Some new approximation methods are proposed for the numerical evaluation of the finitepart singular integral equations defined on Hilbert spaces when their singularity consists of a homeomorphism of the integration interval, which is a unit circle, on itself. Therefore, some existence theorems are proved for the solutions of the finite-part singular integral equations, approximated by several s...

we develop and apply the product integration method to a large class of linear weakly singular volterra systems. we show that under certain sufficient conditions this method converges. numerical implementation of the method is illustrated by a benchmark problem originated from heat conduction.

degenerate kernel approximation method is generalized to solve hammerstein system of fredholm integral equations of the second kind. this method approximates the system of integral equations by constructing degenerate kernel approximations and then the problem is reduced to the solution of a system of algebraic equations. convergence analysis is investigated and on some test problems, the propo...

An integral equations method for a three-dimensional crack in a finite or infinite body is achieved by means of Kupradze potentials. Surface and through cracks can be studied according to this approach with only the assumption that the body has a linear, elastic, homogeneous and isotropic behavior. Both singular surface integrals and line integrals appear in the derived equations. For surface a...

In this study, the existence and uniqueness of the solution of a class of nonlinear finite-part singular integral equations with Carleman shift preserving orientation has been investigated in the generalized Holder space () Γ ϕ H. 1. Introduction Many important problems of engineering mechanics like elasticity, plasticity, and fracture mechanics and aerodynamics can be reduced to the solution o...

This thesis deals with linear ill-posed problems related to compact operators, and iterative Krylov subspace methods for solving discretized versions of these. Linear compact operators in infinite dimensional Hilbert spaces will be investigated and several results on the singular values and eigenvalues for such will be presented. A large subset of linear compact operators consists of integral o...