In this article we obtain asymptotic formulas of arbitrary order for eigenfunctions and eigenvalues of the nonselfadjoint Sturm-Liouville operators with Dirichlet boundary conditions, when the potential is a summable function. Then using these we compute the main part of the eigenvalues in special cases

The scattering of sound by a long cylinder above an impedance boundary Time harmonic electromagnetic scattering from a bounded obstacle: An existence theorem and a computational methodIn this paper we consider the scattering of a wave by concentric penetrable circular cylinder to examine the performance of higher order SRCs up to the L 4 operator in two dimensions. We assume that in the rectangular Cartesian axes, ͑x , y , z͒, the z axis coincides with the axis of a cylinder and an incident wave propagates in a direction perpendicular to the cylinder. All the field quantities are then independent of z.

For all q ∈ (0, 1) and 0 ≤ α < 1 we define a class of analytic functions, so-called q-starlike functions of order α on the open unit disc D = {z : |z| < 1} . We will study this class of functions and explore some inclusion properties with the well-known class Starlike functions of order α.

Asymptotic formulas and numerical estimations for eigenvalues of SturmLiouville problems having singular potential functions, with Dirichlet boundary conditions, are obtained. This study gives a comparison between the eigenvalues obtained by the asymptotic and the numerical methods.

We present in this paper, Bernstein Piecewise Polynomials Method(BPPM), Integral Mean Value Method(IMVM), Taylor Series Method(TSM),The Least Square Method(LSM) are used to solve the integral equations of the second kind numerically. We aim to compare the efficiency of BPPM, IMVM, TSM and LSM in solving the integral equations of the second kind. We solve some examples to illustrate the applicability and simplicity of the methods. The numerical results show that which method is more efficient and accurate. As all these 4 methods consider solutions in numerically it is important to know about their rapidity of convergence to the exact solution.