Search

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 paper, a novel hybrid method is presented for solving the second kind linear Volterra integral equations. Due to the powerful regression ability of least squares support vector regression (LS-SVR), we approximate the unknown function of integral equations by using LS-SVR in intervals with known numerical solutions. The trapezoid quadrature is used to approximate subsequent integrations in intervals with unknown numerical solutions. The feasibility of the proposed method is examined on some integral equations. Experimental results of comparison with analytic and repeated modified trapezoid quadrature method’s solutions show that the proposed algorithm could reach a very high accuracy. The proposed algorithm could be a good tool for solving the second kind linear Volterra integral equations. [Copyright &y& Elsevier]

Abstract: In this study it is shown that the numerical solutions of linear Fredholm integro-differential equations obtained by using Legendre polynomials can also be found by using the variational iteration method. Furthermore the numerical solutions of the given problems which are solved by the variational iteration method obviously converge rapidly to exact solutions better than the Legendre polynomial technique. Additionally, although the powerful effect of the applied processes in Legendre polynomial approach arises in the situations where the initial approximation value is unknown, it is shown by the examples that the variational iteration method produces more certain solutions where the first initial function approximation value is estimated. In this paper, the Legendre polynomial approximation (LPA) and the variational iteration method (VIM) are implemented to obtain the solutions of the linear Fredholm integro-differential equations and the numerical solutions with respect to these methods are compared. [Copyright &y& Elsevier]

Abstract: The evolution equation of a drained aquifer during the consolidation process when time is transformed into the Laplace variable is the modified Helmholtz equation. The governing equation of the steady state of a heterogeneous aquifer which hydraulic conductivity when plotted against depth in a semi-log graph has a constant slope is also the modified Helmhotlz equation. The same equation comes out when the slopes of the hydraulic conductivity plotted against depth and against the hydraulic potential in a semi-log graph are constants. The modified Helmholtz equation will be solved exactly considering a semi-infinite aquifer drained by a circular tunnel. A unique state function, which according to the case considered has different interpretations, is obtained in closed form as an infinite sum involving modified Bessel functions. The amount of water that flows into the tunnel contrarily to the state function may change from case to case and will be calculated exactly and in closed form for the different cited cases. The analytic solution has a wide range of application, is valid for different cases, and within every case needs being adapted to the particular problem to be solved. An illustrative application will show an adaptation of the solution to rock masses when the hydraulic conductivity plotted against the effective stress in a semi-log graph has a constant slope. This will allow estimating the relative precision of approximated formulae for the water inflow in fissured rock masses such as the Zhang and Franklin equation and the first order approximation. [Copyright &y& Elsevier]

Abstract: This note is concerned with the problem of determining approximate solutions of Fredholm integral equations of the second kind. Approximating the solution of a given integral equation by means of a polynomial, an over-determined system of linear algebraic equations is obtained involving the unknown coefficients, which is finally solved by using the least-squares method. Several examples are examined in detail. [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]

Abstract: In this paper, a new method using radial basis function (RBF) networks is presented for solving the linear second kind integral equations of Fredholm and Volterra types. This method employs a growing neural network as the approximate solution of the integral equations, whose the activation functions are RBFs. The parameters (weights, centers and widths) of the approximate solution are adjusted by using an unconstrained optimization problem. Numerical results show that our method has the potentiality to become an efficient approach for solving integral equations. [Copyright &y& Elsevier]

Abstract: It is shown that the differential equation of Smagala and Fawcett [T.G. Smagala, W.R. Fawcett, J. Electroanal. Chem. 597 (2006) 43] for an electrified interface is similar, but not equivalent, to the hypernetted chain approximation integral equation. Nonetheless, their differential equation is of interest and is an improvement over the Poisson–Boltzmann approximation of Gouy and Chapman and may lead to further improvements. [Copyright &y& Elsevier]