For many problems in Physics and Computational Fluid Dynamics (CFD), providing an accurate approximation of derivatives is a challenging task. This paper presents a class of high order numerical schemes for approximating the first derivative. These approximations are derived based on solving a special system of equations with some unknown coefficients. The construction method provides numerous types of schemes with different orders of accuracy. The accuracy of each scheme is analyzed by using Fourier analysis, which illustrates the dispersion and dissipation of the scheme. The polynomial technique is used to verify the order of accuracy of the proposed schemes by obtaining the error terms. Dispersion and dissipation errors are calculated

Abstract

      In this study, we compare between the autoregressive approximations (Yule-Walker equations, Least Squares , Least Squares ( forward- backword ) and Burg’s (Geometric and Harmonic ) methods, to determine the optimal approximation to the time series generated from the first - order moving Average non-invertible process, and fractionally - integrated noise process, with several values for d (d=0.15,0.25,0.35,0.45) for different sample sizes (small,median,large)for two processes . We depend on figure of merit function which proposed by author Shibata in 1980, to determine the theoretical optimal order according to min

Photocatalytic materials are being investigated as effective bactericides due to their superior ability to inactivate a broad range of dangerous microbes. In this study, the following two types of bacteria were employed for bactericidal purposes: Gram-negative Escherichia coli (E. coli) and Gram-positive Staphylococcus aureus (S. aureus). The shape, crystal structure, element percentage, and optical properties of Ag9(SiO4)2NO3 were examined after it was successfully synthesized by a standard mixing and grinding processing route. Bactericidal efficiency was recorded at 100% by the following two types of light sources: solar and simulated light, with initial photocatalyst concentration of 2 µg/mL, and 97% and 95% of bactericidal acti