The Wang-Ball polynomials operational matrices of the derivatives are used in this study to solve singular perturbed second-order differential equations (SPSODEs) with boundary conditions. Using the matrix of Wang-Ball polynomials, the main singular perturbation problem is converted into linear algebraic equation systems. The coefficients of the required approximate solution are obtained from the solution of this system. The residual correction approach was also used to improve an error, and the results were compared to other reported numerical methods. Several examples are used to illustrate both the reliability and usefulness of the Wang-Ball operational matrices. The Wang Ball approach has the ability to improve the outcomes by minimizing the degree of error between approximate and exact solutions. The Wang-Ball series has shown its usefulness in solving any real-life scenario model as first- or second-order differential equations (DEs).
DBN Rashid, IMPAT: International Journal of Research in Humanities, Arts, and Literature, 2016 - Cited by 5
Background: Imaging techniques play a very important role in the specialty of endodontic. The ultrasonographic technique is non-expensive procedure, safe, and reproducible. The aim of the study was to determine the sensitivity, specificity, and accuracy of ultrasound and color Doppler ultrasonography in evaluation of periapical lesions (cyst, granuloma, mixed lesion “cyst within graulomas mass”, and abscess. Subject, Material and method: The sample consists of prospective study for 64 Iraqi participants who attended Karbalaa Specialized Center for Dentistry (males & females). Those patients were diagnosed clinically and radiographically as having periapical lesions of dental origin. They were examined by real time ultrasound and color
... Show MoreThe aim of this paper is to present the numerical method for solving linear system of Fredholm integral equations, based on the Haar wavelet approach. Many test problems, for which the exact solution is known, are considered. Compare the results of suggested method with the results of another method (Trapezoidal method). Algorithm and program is written by Matlab vergion 7.
As the prices of the fuel and power had fluctuated many times in the last decade and new policies appeared and signed by most of the world countries to eliminate global warming and environmental impact on the earth surface and humanity exciting, an urgent need appeared to develop the renewable energy harnessing technologies on the short-term and long-term and one of these promising technologies are the vertical axis wind turbines, and mostly the combined types. The purpose of the present work is to combine a cavity type Savonius with straight bladed Darrieus to eliminate the poor self-starting ability for Darrieus type and low performance for Savonius type and for this purpose, a three-bladed Darrieus type with symmetric
... Show MoreScholars have inherited a tremendous wealth in all sciences and knowledge, especially jurisprudence; therefore, the students of forensic science had to execute this precious heritage, achieving a serious scientific investigation; So I opted for the realization of this part of the Book of Leasing for the small book of fatwas of Yusuf bin Ahmed al-Khasi.
We present a reliable algorithm for solving, homogeneous or inhomogeneous, nonlinear ordinary delay differential equations with initial conditions. The form of the solution is calculated as a series with easily computable components. Four examples are considered for the numerical illustrations of this method. The results reveal that the semi analytic iterative method (SAIM) is very effective, simple and very close to the exact solution demonstrate reliability and efficiency of this method for such problems.
Since the Internet has been more widely used and more people have access to multimedia content, copyright hacking, and piracy have risen. By the use of watermarking techniques, security, asset protection, and authentication have all been made possible. In this paper, a comparison between fragile and robust watermarking techniques has been presented to benefit them in recent studies to increase the level of security of critical media. A new technique has been suggested when adding an embedded value (129) to each pixel of the cover image and representing it as a key to thwart the attacker, increase security, rise imperceptibility, and make the system faster in detecting the tamper from unauthorized users. Using the two watermarking ty
... Show MoreNumerical study has been conducted to investigate the thermal performance enhancement of flat plate solar water collector by integrating the solar collector with metal foam blocks.The flow is assumed to be steady, incompressible and two dimensional in an inclined channel. The channel is provided with eight foam blocks manufactured form copper. The Brinkman-Forchheimer extended Darcy model is utilized to simulate the flow in the porous medium and the Navier-Stokes equation in the fluid region. The energy equation is used with local thermal equilibrium (LTE) assumption to simulate the thermofield inside the porous medium. The current investigation covers a range of solar radiation intensity at 09:00 AM, 12:00 PM, and 04:00
... Show MoreBackground: Determination of sex and estimation of stature from the skeleton is vital to medicolegal investigations. Skull is composed of hard tissue and is the best preserved part of skeleton after death, hence, in many cases it is the only available part for forensic examination. Lateral cephalogram is ideal for the skull examination as it gives details of various anatomical points in a single radiograph. This study was undertaken to evaluate the accuracy of digital cephalometric system as quick, easy and reproducible supplement tool in sex determination in Iraqi samples in different age range using certain linear and angular craniofacial measurements in predicting sex. Materials and Method The sample consisted of 113of true lateral cepha
... Show MoreThe purpose of the present work is to calculate the expectation value of potential energy for different spin states (??? ? ???,??? ? ???) and compared it with spin states (??? , ??? ) for lithium excited state (1s2s3s) and Li- like ions (Be+,B+2) using Hartree-Fock wave function by partitioning techanique .The result of inter particle expectation value shows linear behaviour with atomic number and for each atom and ion the shows the trend ??? < ??? < ??? < ???