For a weakly nonlinear oscillator, the frequency domain Volterra kernels, often called the generalised frequency response functions, can provide accurate analysis of the response in terms of amplitudes and frequencies, in a transparent algebraic way. However a Volterra series representation based analysis will become void for nonlinear oscillators that exhibit subharmonics, and the problem of f...

For a finite but arbitrary precision, we construct efficient low separation rank representations for the Poisson kernel and for the projector on the divergence free functions in the dimension d = 3. Our construction requires computing only one-dimensional integrals. We use scaling functions of multiwavelet bases, thus making these representations available for a variety of multiresolution algor...

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...

In this paper we establish Gauss-type quadrature formulas for weakly singular integrals. An application of the quadrature scheme is given to obtain numerical solutions of the weakly singular Fredholm integral equation of the second kind. We call this method a discrete product-integration method since the weights involved in the standard product-integration method are computed numerically.

in this paper, the solution of a moving volterra-type screw dislocation in an orthotropic layer, bonded between two piezoelectric layers is obtained using complex fourier transform. the dislocation solution is then employed as strain nuclei to derive singular integral equations for a medium weakened by multiple moving cracks. these equations, which are classified as, cauchy singular equations, ...