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 ...

Based on the theory of elasticity, previous analytical solutions concerning a penny-shaped interface crack employ the derivative of the crack surface opening displacements as the primary unknowns, thus leading to singular integral equations with Cauchy-type singularity. The solutions to the resulting integral equations permit only the determination of stress intensity factors and energy release...

The present paper examines the contact problem related to shear punch through a rigid strip bonded to a nonhomogeneous medium. The nonhomogeneous medium is bonded to another nonhomogeneous medium. The strip is perpendicular to the y-axis and parallel to the x-axis. It is assumed that there is perfect bonding at the common plane surface of two nonhomogeneousmedia. Using Fourier cosine transforms...

During the last two-three decades the importance of computer simulations based on numerical full-wave solutions of Maxwell’s has continuously increased in electrical engineering. Software products based on integral equation methods have an unquestionable importance in the frequency domain electromagnetic analysis and design of open-region problems. This paper deals with the surface and volume i...

We construct and analyze a family of well-conditioned boundary integral equations for the Krylov iterative solution of three-dimensional elastic scattering problems by a bounded rigid obstacle. We develop a new potential theory using a rewriting of the Somigliana integral representation formula. From these results, we generalize to linear elasticity the well-known Brakhage-Werner and Combined F...

We present cubature methods approximating the surface integrals arising by Galerkin discretization of boundary integral equations on surfaces in R 3. This numerical integrator does not depend on the explicit form of the kernel function, the trial and test space, or the surface parametrization. Thus, it is possible to generate the system matrix for a broad class of integral equations just by rep...

In this paper, the possibilities of finding out surface plasmons in negative-permittivity metamaterial scatterers, using surface integral equations, are discussed. Electrostatic resonances manifest themselves as very high values of the polarizability for a certain (negative) value of the permittivity. Another way to locate the position of the resonances is to calculate the eigenvalues of the so...

where p and q are points on S, G is the free-space Green’s function, ∂/∂nq denotes normal differentiation at q, and uinc is the incident field. The Helmholtz integral equations are familiar boundary integral equations, for which there is a complete theoretical framework (Kleinman and Roach, 1974; Colton and Kress, 1983). Many examples of their numerical treatment, usually using boundary element...

‎‎In this paper, Solvability nonlinear Volterra integral equations with general vanishing delays is stated. So far sinc methods for approximating the solutions of Volterra integral equations have received considerable attention mainly due to their high accuracy. These approximations converge rapidly to the exact solutions as number sinc points increases. Here the numerical solution of nonlinear...