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

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

Biosorption is an effective method to remove toxic metals from wastewaters. In this study biosorption of lead and chromium ions from solution was studied using Citrobacter freundii and Citrobacter kosari isolated from industrial wastewater. The experimental results showed that optimum grwoth temperature for both bacteria is 30oC and the optimum pH is 7 &6 for C. freundii and C. kosari respectively. While the optimum incubation period to remove Pb and Cr for C. freundii and C. kosari is 4 days and 3days respectively. Also the biosorption of Pb and Cr in mixed culture of bacteria and mixed culture of Pb and Cr was investigated. Result indicate that uptake of Cr and Pb for C.freundii, C. kosari and in mixes culture of both bacteria is 58%, 53%

The present study aims to remove nickel ions from solution of the simulated wastewater using (Laminaria saccharina) algae as a biosorbent material. Effects of experimental parameters such as temperature at (20 - 40) C⁰, pH at (3 - 7) at time (10 - 120) min on the removal efficiency were studied.
Box-Wilson method was adopted to obtain a relationship between the above three experimental parameters and removal percentage of the nickel ions. The experimental data were fitted to second order polynomial model, and the optimum conditions for the removal process of nickel ions were obtained.
The highest removal percentage of nickel ions obtained was 98.8 %, at best operating conditions (Temperature 35 C⁰, pH 5 and Time 10 min).