Purpose: The purpose of this work is to present an APPROXIMATION for singular integrals of Cauchy type kernel on a smooth-oriented contour.Methods: For the method, we use a small modification of the spline functions in order to eliminate the singularity. Noting that this APPROXIMATION is due to the idea of Sanikidze’s Approximate solution of singular integral equations in the case of closed contours of integrations.Results: This APPROXIMATION represents a good approach for any singular integral given on the curve in the sense of Cauchy principal value.Conclusions: This APPROXIMATION is destined to solve numerically the singular integral equations with Cauchy type kernel on a smooth-oriented contour.

This paper presents a modified method for approximating systems by a sequence of ‎LINEAR time varying systems. The convergence proof is outlined and the potential of ‎this methodology is discussed. Simulation results are used to show the effectiveness ‎of the proposed method‏.‏

This study proposes a new LINEAR APPROXIMATION for solving the dynamic response equations of a rocking rigid block. LINEARization assumptions which have already been used by Hounser and other researchers cannot be valid for all rocking blocks with various slenderness ratios and dimensions; hence, developing new methods which can result in better APPROXIMATION of governing equations while keeping simplicity is necessary. In this paper, a new LINEAR APPROXIMATION is derived for solving the deferential equations of a rocking block in order to include wider range of blocks with various slenderness. The proposed method is verified by numerical solutions of the governing equations utilizing two methods of: average acceleration and fourth order Runge-Kutta. Verifications revealed more reasonable accuracy of the proposed method in comparison with the current LINEARization assumptions.

This paper presents a new fingerprint coding technique using non-LINEAR APPROXIMATION of multiwavelet coefficients followed by multi-stage vector quantization. Fingerprints contain oscillatory patterns in the vertical, horizontal and diagonal direction. Wavelet transform often fails to accurately capture the oscillatory patterns in the fingerprints, especially at low bit rates. Due to implementation constraints scalar wavelets do not posses all the properties such as orthogonality, short support, LINEAR phase symmetry, and a high order of APPROXIMATION through vanishing moments simultaneously, which are very much essential for efficient image compression. New class of wavelets called ‘Multiwavelets’ which posses more than one scaling function overcomes this problem. The effective multiwavelet coefficients are quantized by multistage vector quantization which can achieve very low encoding and storage complexity in comparison to unstructured vector quantization. Entropy coding of quantized coefficients is done using Huffman coding. The performance of the proposed scheme is compared with the results obtained from scalar wavelets. The performance of the proposed scheme is better than the existing wavelet based coding at low bit rate.

The functioning of a thermoelectric system in a stationary mode is often inefficient because it does not allow flexible control of the temperature regime. The design of thermoelectric devices and systems in transient modes requires identifying their dynamic models, first of all, the control object – the Peltier thermoelectric module. As a rule, well-known identification techniques involve calculating the parameters of a fractional-rational transfer function (or, equivalently, an autoregressive model) of the object of control. At the same time, the increase in the accuracy of identification requirements is associated with significant computational costs. The proposed identification technique requires the determination of the time dependencies of the control current and temperature deviation, the calculation of their spectra based on piecewise LINEAR APPROXIMATION, and the calculation of the transfer coefficient as the ratio of the spectra of the output and input signals. The calculated relations of piecewise LINEAR approximating functions, spectral densities, and time forms of input and output parameters of the model under study are presented. The amplitude and phase frequency response of the Peltier module are calculated. The low RMS error in the identification of the amplitude-frequency characteristic and phase-frequency characteristic showed the effectiveness of the proposed identification technique.

It is well-known that the matrix equations play a significant role in several applications in science and engineering. There are various approaches either direct methods or iterative methods to evaluate the solution of these equations. In this research article, the ho-motopy perturbation method (HPM) will employ to deduce the approximated solution of the LINEAR matrix equation in the form AXB=C. Furthermore, the conditions will be explored to check the convergence of the homotopy series. Numerical examples are also adapted to illustrate the properties of the modified method.

In this paper, the interpolating moving least-squares (IMLS) method is discussed. The interpolating moving least square methodology is an e, ective technique for the APPROXIMATION of an unknown function by using a set of disordered data. Then we apply the IMLS method for numerical solution of Volterra{Fredholm integral equations, and , nally some examples are given to show the accuracy and applicability of the method.

The aim of this paper is to present a numerical approach for solving LINEAR and nonLINEAR differential equations arising in astrophysics, commonly known as Lane-Emden equations. The proposed method is based on the collocation method and first involves taking the truncated Chelyshkov series of the function in the equation. The computational cost is reduced due to the orthogonality of Chelyshkov polynomials, and the solution of a LINEAR or nonLINEAR Lane-Emden equation is reduced to solving a system of LINEAR or nonLINEAR algebraic equations. Several test examples of these types of differential equations, modeling different physical problems with initial and boundary conditions, are solved to demonstrate the reliability of the method. To demonstrate its effectiveness, absolute error tables and graphs are presented, and the numerical results are compared with other methods and exact solutions. It is observed that when the exact solution has a polynomial form, the proposed method proves to be highly accurate and effective.