In this paper, we propose the triangular orthogonal functions as a basis functions
 for solution of weakly singular Volterra integral equations second
 kind. Powerful properties these and some operational matrices
 are utilized in direct method to reduce equation to
 algebraic equations. The presented does not need any integration
 obtaining constant coefficients. is co...

This article considers weakly singular, singular and hypersingular integrals, which arise when the boundary integral equation (BIE) methods are used to solve problems in science and engineering. For their regularization, an approach based on the theory of distribution and application of the Green theorem has been used. The expressions, which allow an easy calculation of the weakly singular, sin...

We consider a fractional order viscoelasticity problem modelled by power-law type stress relaxation function. This viscoelastic is Volterra integral equation of the second kind with weakly singular kernel where convolution corresponds to differentiation/integration. use spatial finite element method and difference scheme in time. Due weak singularity, integration time managed approximately line...

In this paper, the well known iterated Galerkin method and iterated Galerkin-Kantorovich regularization method for approximating the solution of Fredholm integral equations of the second kind are generalized to Hammerstein equations with smooth and weakly singular kernels. The order of convergence of the Galerkin method and those of superconvergence of the iterated methods are analyzed. Numeric...

Abstract In this study, we applied an advanced barycentric Lagrange interpolation formula to find the interpolate solutions of weakly singular Fredholm integral equations second kind. The kernel is interpolated twice concerning both variables and then transformed into product five matrices; two them are monomial basis matrices. To isolate singularity kernel, developed techniques based on a good...

In this paper we establish weighted norm inequalities for singular integral operators with kernel satisfying a variant of the classical Hörmander’s condition.