The numerical treatment of integral equations pdf

Click here to sign up. Download Free PDF. On the numerical treatment of the contact problem International Journal of Mathematics and Mathematical Sciences, Abdallah Badr. A short summary of this paper. On the numerical treatment of the contact problem. The problem of the contact of two elastic bodies of arbitrary shape with a kernel in the form of a logarithmic function—which is investigated from Hertz problem—is reduced to an integral equation.

A numerical method is adapted to determine the pressure between the two surfaces under certain conditions. Keywords and phrases. Hertz problem, integral equation, orthogonal polynomials.

Primary 45B Integral equa- tion containing singular kernel appears in studies involving airfoil [3], fracture me- chanics contact [18] radiation and molecular conduction [6] and others. Over the past thirty years, substantial progress has been made in developing innovative approxi- mate analytical and purely numerical solution to a large class of Fredholm integral equation with singular kernel.

Since closed form solution to these in- tegral equations are generally not available, great attention has been focused on the numerical treatment. For example in [7] Gerasoulis used a piecewise quadratic polynomials in the solution of the singular integral equation. As the same way of Gerasoulis, Miller and Keer [12] obtained the solution of the integral equation with Cauchy kernel. In [17] Venturino used Galerkin method to obtain the singular integral equation of the second kind with Cauchy kernel.

In this paper, a numerical method is used to obtain the potential function of a Fred- holm integral equation of the second kind with Cauchy kernel. The solution of the problem reduces to the solution of a linear system. At the end, we give a numerical application to test our method. BADR 2. Formulation of the contact problem. Here denotes integration with Cauchy principal value sense. Abdou and Hassan [2] used potential theory to obtain the eigenvalues and eigenfunctions of the problem.

Solution of the problem. In this section, we will solve equation 2. To browse Academia. Log in with Facebook Log in with Google. Remember me on this computer. Enter the email address you signed up with and we'll email you a reset link. Need an account? Click here to sign up. Download Free PDF. Lijuan Li. A short summary of this paper. The influence of lossy ground is taken into account via Fresnel space-time reflection coefficient.

The integral equations are solved efficiently by method of moments combined with marching on in time procedure. The calculated results agree with those of references. The method is also verified by the experiment in near field.

Mean- while, the TD numerical techniques are often concerned with wires in free space or above a perfectly conducting half-space [2]. Single conductor wire in free space. In this paper, the TDIE of thin wire conductors in the half-space configurations is converted into a simple form by using only vector magnetic potential and solved by means of the method of moments MOM and the marching on in time MOT procedure.

Several thin wire structures in the half-space configurations have been dealt with, such as a single wire excited by external electromagnetic pulse in the presence of perfect conducting and dissipative ground, two coupled horizontal wires in a two media configuration and wires buried in the dielectric half-space. These models can be widely used Fig. Single wire above ground. Calculated results are where agreeable with those in references and tested in near field.

The current is induced by the thin-wire ap- 4 proximation. Applying the boundary condition for the total elec- tric field, 1 could be changed into where is the equivalent axial current to be determined, 2 is the tangential incident field, is the velocity of light, and are, respectively, the length and radius of the wire.

Single buried wire scatter. Coupled conductor wires above ground. Select All Expand All. Collapse All. Citation Export Print. Javascript must be enabled for narrowing. Results 1 - 1 of 1. Search took: 0.

Numerical treatment of Faddeev integral equations for non-separable potentials. Eyre, D. National Research Inst. Abstract Abstract. Two-dimensional integral equations are approximated in a trial space of piecewise quadratic polynomials.

Approximate solutions are obtained for a model problem of three spinless bosons interacting via the sum of S-wave Yukawa potentials. Numerical estimates for rates of convergence of the method are obtained.