Abstract The paper deals with the numerical solution of 2D wave propagation exterior problems including viscous and material damping coefficients equipped by Neumann boundary condition, hence modeling hard scattering damped waves. differential problem, which includes, besides diffusion, advection reaction terms, is written as a space–time integral equation (BIE) whose kernel given hypersingular...

A new hypersingular integro-differential equation is considered on a closed curve located the complex plane. The refers to linear equations with variable coefficients of special kind. characteristic feature presence constant multipliers in coefficients, given by some recurrent relations. first reduced solving Riemann boundary value problem original curve. class functions established for problem...

planar d-bar integral equation is one of the inverse scattering solution methods for complex problems including inverse conductivity considered in applications such as electrical impedance tomography (eit). recently two different methodologies are considered for the numerical solution of d-bar integrals equation, namely product integrals and multigrid. the first one involves high computational ...

In this paper, recent development of the dual BEM in acoustic problem is presented. The role of hypersingular integral equation in the dual BEM for the problems with a degenerate boundary is examined. First, the dual integral formulation is proposed. Based on the formulation, we develop four methods ± the complex-valued dual BEM, the real-part dual BEM, the real-valued dual MRM, and the complet...

The polar coordinate transformation (PCT) method has been extensively used to treat various singular integrals in the boundary element method (BEM). However, the resultant integrands of the PCT tend to become nearly singular when (1) the aspect ratio of the element is large or (2) the field point is closed to the element boundary; thus a large number of quadrature points are needed to achieve a...

In this paper, we present a method for solving the rst kind Abel integral equation. In thismethod, the rst kind Abel integral equation is transformed to the second kind Volterraintegral equation with a continuous kernel and a smooth deriving term expressed by weaklysingular integrals. By using Sidi's sinm - transformation and modied Navot-Simpson'sintegration rule, an algorithm for solving this...

where wα,β(x) = |x|αe−|x| β is a generalized Freud weight with α ≥ 0, β > 1 and 0 ≤ p ∈ N. This topic is of interest, for instance, in the numerical solution of hypersingular integral equations, which are often models for physics and engineering problems (see [5, 2, 4]). To our knowledge, most of the papers available in the literature deal with the approximation of Hadamard integrals on bounded...