This paper presents a new set of boundary integral equations for three dimensional acoustic shape sensitivity analysis based on the direct differentiation method. A linear combination of the derived equations is used to avoid the fictitious eigenfrequency problem associated with the conventional boundary integral equation method when solving exterior acoustic problems. The strongly singular and...

In this contribution we deal with the development, theoretical examination and numerical examples of a method of lines approximation for the Cauchy problem for elliptic partial differential equations. We restrict ourselves to the Laplace equation. A more general elliptic equation containing a diffusion coefficient will be considered in a forthcoming paper. Our main results are the regularizatio...

this paper presents some results concerning the existence of solutions for a functional integral equation of volterra type in two variables, via measure of noncompactness. two examples are included to illustrate the main result.

Given a function f holomorphic at infinity, the n-th diagonal Padé approximant to f, denoted by [n/n]f, is a rational function of type (n,n) that has the highest order of contact with f at infinity. Nuttall’s theorem provides an asymptotic formula for the error of approximation f− [n/n]f in the case where f is the Cauchy integral of a smooth density with respect to the arcsine distribution on [...

We consider a macroscopic (drift-diffusion) model describing a simple microwave generator, consisting of a special type of semiconductor material that, when biased above a certain threshold voltage, generates charge waves. These waves correspond to travelling wave solutions of the model equation which, however, turn out to be unstable in a standard formulation of the travelling wave problem. He...

Given function f holomorphic at infinity, the n-th diagonal Padé approximant to f , say [n/n]f , is a rational function of type (n,n) that has the highest order of contact with f at infinity. Equivalently, [n/n]f is the n-th convergent of the continued fraction representing f at infinity. BernsteinSzegő theorem provides an explicit non-asymptotic formula for [n/n]f and all n large enough in the...

A Sine function approach is used to derive a new Hunter type quadrature rule for the evaluation of Cauchy principal value integrals of certain analytic functions. Integration over a general arc in the complex plane is considered. Special treatment is given to integrals over the interval (-1, 1). It is shown that the quadrature error is of order 0(e~ ), where N is the number of nodes used, and w...

It is well known that the parabolic partial differential equations in two or more space dimensions with overspecified boundary data, feature in the mathematical modeling of many phenomena. In this article, an inverse problem of determining an unknown time-dependent source term of a parabolic equation in general dimensions is considered. Employing some transformations, we change the inverse prob...