We shall study a weak solution in the Sobolev space of the transmission problem for the Laplace equation using the integral equation method. First we use the indirect integral equation method. We look for a solution in the form of the sum of the double layer potential corresponding to the skip of traces on the interface and a single layer potential with an unknown density. We get an integral eq...

boundary integral equations (bie) are reformulations of boundary value problems for partial differential equations. there is a plethora of research on numerical methods for all types of these equations such as solving by discretization which includes numerical integration. in this paper, the neumann problem is reformulated to a bie, and then moving least squares as a meshless method is describe...

a complex of cu(ii) with 1-(6-hydroxynaphthalen-2-yl) butane-1,3-dione (hnbd) was synthesized and characterized by elemental analysis, ir, uv and dta-tg-dtg techniques.    ir spectra as well as uv-visible absorption measurements indicated that cu(ii) ion was coordinated to the hnbd ligand. the tg-dta-dtg curves showed that thermal decomposition of the anhydrous complex was a two-stage process a...

In this paper, a special technique is studied by using the orthogonal Chebyshev polynomials to get approximate solutions for singular and hyper-singular integral equations of the first kind. A singular integral equation is converted to a system of algebraic equations based on using special properties of Chebyshev series. The error bounds are also stated for the regular part of approximate solut...

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...

The applied electrical field destroys the spherical symmetry of the field less Barker-Ferry equation. The dimensionality of the task increases and furthermore no general integration domain can be specified due to the correlation of the phase space and time coordinates. In this part of the work we propose and integral formulation which decouples these coordinates. The equation is solved by the r...