The aim of this paper is to present a method for solving high order ordinary differential equations with two point's boundary condition, we propose semi-analytic technique using two-point oscillatory interpolation to construct polynomial solution. The original problem is concerned using two-point oscillatory interpolation with the fit equal numbers of derivatives at the end points of an interval [0 , 1] . Also, many examples are presented to demonstrate the applicability, accuracy and efficiency of the method by comparing with conventional methods.

Volterra – Fredholm integral equations (VFIEs) have a massive interest from researchers recently. The current study suggests a collocation method for the mixed Volterra - Fredholm integral equations (MVFIEs)."A point interpolation collocation method is considered by combining the radial and polynomial basis functions using collocation points". The main purpose of the radial and polynomial basis functions is to overcome the singularity that could associate with the collocation methods. The obtained interpolation function passes through all Scattered Point in a domain and therefore, the Delta function property is the shape of the functions. The exact solution of selective solutions was compared with the results obtained

Cooling towers is one of the most important unit in industry, they are used to dispose heat from cooling media used in the integrated units. The choice of the cooling media plays recently an important rule due to fresh-water scarcity. The use of saline as a cooling media become of growing interest, but the corrosion problem has to be taken in consideration. In this study the simultaneous effect of cooling tower operation parameters on the corrosion rate of mild-steel is considered. The role of NaCl content is found to be pronounced more than the working solution temperature and flowrate. The corrosion of mild-steel in these studied factors had shown an interesting result especially with the NaCl% content. Firstly, there was an increase in t

In this paper we use non-polynomial spline functions to develop numerical methods to approximate the solution of 2nd kind Volterra integral equations. Numerical examples are presented to illustrate the applications of these method, and to compare the computed results with other known methods.

In this study, a new technique is considered for solving linear fractional Volterra-Fredholm integro-differential equations (LFVFIDE's) with fractional derivative qualified in the Caputo sense. The method is established in three types of Lagrange polynomials (LP’s), Original Lagrange polynomial (OLP), Barycentric Lagrange polynomial (BLP), and Modified Lagrange polynomial (MLP). General Algorithm is suggested and examples are included to get the best effectiveness, and implementation of these types. Also, as special case fractional differential equation is taken to evaluate the validity of the proposed method. Finally, a comparison between the proposed method and other methods are taken to present the effectiveness of the proposal meth

A batch adsorption system was applied to study the adsorption of methylene blue from aqueous solution by Iraqi bentonite and treated bentonite with different amount of zinc oxide (ZnO). The adsorption capacities of methylene blue onto bentonite were evaluated. The equilibrium between liquid and solid phase was described by Langmuir model better than the Freundlich model. Langmuir and Freundlich constants have been determined. The separation factor or equilibrium parameter, RL which is used to predict if an adsorption system is favourable or unfavourable was calculated for all cases.

The present work is devoted to investigate the performance of a homemade Y-shape catalytic microreactor for degradation of dibenzothiophene (DBT), as a model of sulphur compounds including in gas oil, utilizing solar incident energy. The microchannel was coated with TiO2 nanoparticles which were used as a photocatalyst. Performance of the microreactor was investigated using different conditions (e.g., DBT concentration, LHSV, operating temperature, and (H₂O₂/DBT) ratio). Our experiments show that, in the absence of UV light, no reaction takes place. The results revealed that outlet concentration of DBT decreases as the mean residence time in the microreactor increases. Also, it was noted that operating temperature s

 This project introduces a prospective material for photonic laser applications. The material is olive oil which is classified as organic compound, having a good nonlinear optical properties candidate to be used in photonic applications. A high purity sample of olive oil has been used. The theoretical calculation to generate third harmonic wave using olive oil has been determine using MATLAB program. THG (λ=355nm) intensity has been determined at two cases of sample thicknesses 1mm and 10mm. The minimum threshold incident intensity to obtain THG intensity are equal I_ω=7530 mW/cm² at L=1mm and I_ω= 6220 mW/cm² at L=10mm. The possibility of generation of third harmonic in olive oil inside