The research aims to find approximate solutions for two dimensions Fredholm linear integral equation. Using the two-variables of the Bernstein polynomials we find a solution to the approximate linear integral equation of the type two dimensions. Two examples have been discussed in detail.
Nisoldipine (NSD) is a dihydropyridine class of calcium channel blockers used for hypertension treatment, it belongs to class II BCS (low solubility with high permeability), its absolute bioavailability is only 5% due to presystemic metabolism in the gut wall. It is also a substrate for a CYP3A and P-gp. Bilosomes are lipid bilayer vesicles incorporating bile salts in their walls to prevent degredation by GIT bile salts. The aim of this study is to prepare nisoldipine bilosomes as vesicular carrier and assess the effect of different formulation variables such as type of surfactant, amount of cholesterol, surfactant and sonication time on particle size, entrapment efficiency and poly dispersity index of the prepared bilos
... Show MoreIn this paper,the homtopy perturbation method (HPM) was applied to obtain the approximate solutions of the fractional order integro-differential equations . The fractional order derivatives and fractional order integral are described in the Caputo and Riemann-Liouville sense respectively. We can easily obtain the solution from convergent the infinite series of HPM . A theorem for convergence and error estimates of the HPM for solving fractional order integro-differential equations was given. Moreover, numerical results show that our theoretical analysis are accurate and the HPM can be considered as a powerful method for solving fractional order integro-diffrential equations.
... Show MoreEvaluation is one of the most important elements of teaching process. The recent trends in evaluation and educational reform movements have called for using alternative evaluation, which focuses on performance evaluation. Authentic assessment is usually described as formative, in which students participate in their acquisition, in addition to the fact that students are productive and active, which is reflected in the students' achievement and skill level. The study aims to reveal the degree of knowledge and use of alternative assessment tools by primary school teachers in Gaza -Palestine. To meet the objective of the study, the researchers used the descriptive-analytical method and the questioner as a study tool. The study sample c
... Show MoreThe method of operational matrices is based on the Bernoulli and Shifted Legendre polynomials which is used to solve the Falkner-Skan equation. The nonlinear differential equation converting to a system of nonlinear equations is solved using Mathematica®12, and the approximate solutions are obtained. The efficiency of these methods was studied by calculating the maximum error remainder ( ), and it was found that their efficiency increases as increases. Moreover, the obtained approximate solutions are compared with the numerical solution obtained by the fourth-order Runge-Kutta method (RK4), which gives a good agreement.
Many numerical approaches have been suggested to solve nonlinear problems. In this paper, we suggest a new two-step iterative method for solving nonlinear equations. This iterative method has cubic convergence. Several numerical examples to illustrate the efficiency of this method by Comparison with other similar methods is given.