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In this work, we have used the integral equations method to compute the surface tension of several refrigerant mixtures. For this goal, we have employed the Stockmayer potential and examined theoretically the surface tension of several pure refrigerants like R134a, R32, R125, R152a, R1234yf, R1234ze and also refrigerant mixtures such as R32 + R125, R32 + R134a, R125 + R134a, R125 + R143a, and R143a + R134a, R125 + R152a, R134a + R152a, R32 + R1234ze, R32 + R1234yf and R290 + R600a. We have solved numerically the Ornstein−Zernike (OZ) equation using the hypernetted chain approximation (HNC) for binary refrigerant mixtures and obtained the radial distribution functions. Finally, the variation of surface tension as a function of temperature is studied using a new molecular thermodynamic model and the obtained results have been compared with available results. Our theoretical results show a fairly agreement with available data except for R290 + R600a. [ABSTRACT FROM AUTHOR]

In this paper, a numerical method is proposed to approximate the solution of a two-dimensional scattering problem of time-harmonic elastic wave from a rigid obstacle. By Helmholtz decomposition, the scattering problem is reduced to a system of Helmholtz equations with coupled boundary conditions. Then, we prove that the system of Helmholtz equations has only one solution under certain conditions, and propose an integral equation method to solve it numerically based on Tikhonov regularization method. Finally, numerical examples are presented to show the feasibility and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

We build a numerical approximation method, for Fredholm integral equation solution of the second type. This method is based on the regularization by convolution and Fourier series expansion. It provides a better convergence order. [ABSTRACT FROM AUTHOR]

We show that, by correctly selecting the probability distribution function p ( s ) for a particle’s distance-to-collision, the nonclassical diffusion equation can be represented exactly by the nonclassical linear Boltzmann equation for an infinite homogeneous medium. This choice of p ( s ) preserves the true mean-squared free path of the system, which sheds new light on the results obtained in previous work. [ABSTRACT FROM AUTHOR]

Abstract: In order to compute an approximate solution of a weakly singular integral equation, we first regularize the kernel and then truncate the associated Fourier series. Applications to Green and Abel operators are given. [Copyright &y& Elsevier]

Abstract: In this work, a functional approximation method for calculating the linear functional of the solution of second-kind Fredholm integral equations is developed. When the method is applied to the collocation method or to the multi-projection method, it generates approximations which exhibit superconvergence. [Copyright &y& Elsevier]