We present a reliable algorithm for solving, homogeneous or inhomogeneous, nonlinear ordinary delay differential equations with initial conditions. The form of the solution is calculated as a series with easily computable components. Four examples are considered for the numerical illustrations of this method. The results reveal that the semi analytic iterative method (SAIM) is very effective, simple and very close to the exact solution demonstrate reliability and efficiency of this method for such problems.

This study aims to show the  effectiveness of immobilization of Chlorella green algae biomass in the form of bead for the removal of lead ions from synthetic polluted water  at various operational parameters such as pH (2–6), biosorbent dosage (0.5–20 g/L) and initial concentration (10–100 mg/L). More than 90 % removal efficiency was achieved. FTIR and SEM-EDX analysis of the biosorbent before and after sorption show differences in the functional groups on the adsorbent surface. Langmuir and Freundlich equilibrium isotherm, pseudo-first-order and pseudo-second-order kinetic models were applied to the experimental and results and show good conformity with Langmuir isotherm model and pseudo-second-order kinetic model with c

 This studies deals with investigated the potential of a Iraqi bentonite clay for the adsorption of bromo phenol red dye from contaminated water. Impulse adsorption experiments were performed. The contact time influence of initial dye concentration, temperature, pH, ionic strength, partical size adsorbent  and adsorbent dosage on bromo phenol red  adsorption  are investigated in a series of batch adsorption experiments. Adsorption equilibrium data were analyzed and described by the Freundlich, Langmuir and temkin isotherms equations. Thermodynamic parameters inclusive the Gibbs free energy (∆G•), enthalpy (∆H•), and entropy (∆S•), were also calculated. These parameters specified tha

This research presents a study for precipitating phosphorus (as phosphate ion) from simulated wastewater (5ppm initial concentration of phosphorus) using calcium hydroxide Ca(OH)₂ solution. The removal of phosphorus by Ca (OH)₂ solution is expected to be very effective since the chemical reaction is of acid-base type but Ca(OH)₂ forms complex compound with phosphate ions called. Hydroxyapatite Ca₅ (PO₄)₃OH. hydroxyapatite is slightly soluble in water. This research was directed towards sustainable elements as phosphorus. Kinetics of the dissolution reaction of hydroxyapatite was investigated to find the best factors to recover phosphorus. The effect of con

In this research, hand lay- up technique is used to prepare samples from epoxy resin reinforced with multi- walled carbon nanotubes in different weight fractions (0, 2, 3, 4, 5) wt%. The immersion effect by sodium hydroxide solution (NaOH) at normality (0.3N) for a period of (15 days) on the thermal conductivity of nanocomposites was studied, and compared to natural condition (before immersion). The thermal conductivity of epoxy nanocomposites specimens were carried out using Lee’s disk method. The experimental results showed that thermal conductivity increased with increase weight fraction before and after immersion for all specimens, while the immersion effect leads to decrease thermal conductive values compared to thermal conductivi

The object of this study was to evaluate the efficiency of safranin O (SFO), dye removal with application of Thuja orientalis as a low-cost biosorbent. The biosorption equilibrium level was determined as a function of pH, adsorbent dose, contact time and temperature. Surface area and pore size distribution were measured for the adsorbent. Thuja has a good removal effeciency for SFO dye. The adsorption kinetics data were best fit for the pseudo-second order kinetic (the regression coefficient = 0.999). The experimental equilibrium adsorption data are tested for the Langmuir, freundlich,Temkin and Dubinin-Radushkevich isotherm modles. From the values of the regression coefficient the results indicate the following order to fit the isotherm

To obtain the approximate solution to Riccati matrix differential equations, a new variational iteration approach was ‎proposed, which is suggested to improve the accuracy and increase the convergence rate of the approximate solutons to the ‎exact solution. This technique was found to give very accurate results in a few number of iterations. In this paper, the ‎modified approaches were derived to give modified solutions of proposed and used and the convergence analysis to the exact ‎solution of the derived sequence of approximate solutions is also stated and proved. Two examples were also solved, which ‎shows the reliability and applicability of the proposed approach. ‎

This research presents the possibility of using banana peel (arising from agricultural production waste) as biosorbent for removal of copper from simulated aqueous solution. Batch sorption experiments were performed as a function of pH, sorbent dose, and contact time. The optimal pH value of Copper (II) removal by banana peel was 6. The amount of sorbed metal ions was calculated as 52.632 mg/g. Sorption kinetic data were tested using pseudo-first order, and pseudo-second order models. Kinetic studies showed that the sorption followed a pseudo second order reaction due to the high correlation coefficient and the agreement between the experimental and calculated values of q_e. Thermodynamic parameters such as enthalpy change (ΔH

The integral transformations is a complicated function from a function space into a simple function in transformed space. Where the function being characterized easily and manipulated through integration in transformed function space. The two parametric form of SEE transformation and its basic characteristics have been demonstrated in this study. The transformed function of a few fundamental functions along with its time derivative rule is shown. It has been demonstrated how two parametric SEE transformations can be used to solve linear differential equations. This research provides a solution to population growth rate equation. One can contrast these outcomes with different Laplace type transformations

This article addresses a new numerical method to find a numerical solution of the linear delay differential equation of fractional order , the fractional derivatives described in the Caputo sense. The new approach is to approximating second and third derivatives. A backward finite difference method is used. Besides, the composite Trapezoidal rule is used in the Caputo definition to match the integral term. The accuracy and convergence of the prescribed technique are explained. The results  are shown through numerical examples.