In this paper, three approximate methods namely the Bernoulli, the Bernstein, and the shifted Legendre polynomials operational matrices are presented to solve two important nonlinear ordinary differential equations that appeared in engineering and applied science. The Riccati and the Darcy-Brinkman-Forchheimer moment equations are solved and the approximate solutions are obtained. The methods are summarized by converting the nonlinear differential equations into a nonlinear system of algebraic equations that is solved using Mathematica®12. The efficiency of these methods was investigated by calculating the root mean square error (RMS) and the maximum error remainder (𝑀𝐸𝑅n) and it was found that the accuracy increases with increasi

Here, we found an estimation of best approximation of unbounded functions which satisfied weighted Lipschitz condition with respect to convex polynomial by means of weighted Totik-Ditzian modulus of continuity

The aerodynamic characteristics of the forward swept wing aircraft have been studied theoretically and experimentally. Low order panel method with the Dirichlet boundary condition have been used to solve the case of the steady, inviscid and compressible flow. Experimentally, a model was manufactured from wood to carry out the tests. The primary objective of the experimental work was the measurements of the wake dimensions and orientation, velocity defect along the wake and the wake thickness. A blower type low speed (open jet) wind tunnel was used in the experimental work. The mean velocity at the test section was (9.3 m/s) and the Reynolds number based on the mean aerodynamic chord and the mean velocity was (0.46x105). The measurements sho

The effect of gamma rays on males and females ofCallasobruchus maculatus and Trogoderma granarium which were irradiated as 1-3 days old adults was investigated. The results revealed that the percent egg hatch for both pests was zero ,and average number of egg (34.2,21.5) for both pests respectively where their males where irradiated with 0.18 kGy and mated with unirradiated females. While the percent of egg hatch and the average number of egg (zero,21,3) respectively when the females where irradiated with 0.18 and 0.15 kGy and mated to unirradiated males for C. maculatus and T. granarium respectively. Furthermore, the results showed that the percent of eggs hatch and average number of egg was ( zero,22.7) for C. maculatus when both sexes i

This article deals with the approximate algorithm for two dimensional multi-space fractional bioheat equations (M-SFBHE). The application of the collection method will be expanding for presenting a numerical technique for solving M-SFBHE based on “shifted Jacobi-Gauss-Labatto polynomials” (SJ-GL-Ps) in the matrix form. The Caputo formula has been utilized to approximate the fractional derivative and to demonstrate its usefulness and accuracy, the proposed methodology was applied in two examples. The numerical results revealed that the used approach is very effective and gives high accuracy and good convergence.

Discotic liquid crystal compounds were synthesized and characterized. Liquid crystalline texture of these compounds was investigated by polarized optical microscopy (POM). The Hartree-Fock approximation (HF) was used to calculate theoretical molecular parameters for synthesized compounds such as optimization, hardness, EHOMO, ELUMO, and energy gap using the Gaussian 09W program.

Based on analyzing the properties of Bernstein polynomials, the extended orthonormal Bernstein polynomials, defined on the interval [0, 1] for n=7 is achieved. Another method for computing operational matrices of derivative and integration D_b and R_(n+1)^B respectively is presented. Also the result of the proposed method is compared with true answers to show the convergence and advantages of the new method.