In this research, Haar wavelets method has been utilized to approximate a numerical solution for Linear state space systems. The solution technique is used Haar wavelet functions and Haar wavelet operational matrix with the operation to transform the state space system into a system of linear algebraic equations which can be resolved by MATLAB over an interval from 0 to . The exactness of the state variables can be enhanced by increasing the Haar wavelet resolution. The method has been applied for different examples and the simulation results have been illustrated in graphics and compared with the exact solution.

The main work of this paper is devoted to a new technique of constructing approximated solutions for linear delay differential equations using the basis functions power series functions with the aid of Weighted residual methods (collocations method, Galerkin’s method and least square method).

In this paper, Touchard polynomials (TPs) are presented for solving Linear Volterra integral equations of the second kind (LVIEs-2k) and the first kind (LVIEs-1k) besides, the singular kernel type of this equation. Illustrative examples show the efficiency of the presented method, and the approximate numerical (AN) solutions are compared with one another method in some examples. All calculations and graphs are performed by program MATLAB2018b.

A new method based on the Touchard polynomials (TPs) was presented for the numerical solution of the linear Fredholm integro-differential equation (FIDE) of the first order and second kind with condition. The derivative and integration of the (TPs) were simply obtained. The convergence analysis of the presented method was given and the applicability was proved by some numerical examples. The results obtained in this method are compared with other known results.

Microbial fuel cell is a device that uses the microorganism metabolism for the production of electricity under specific operating conditions. Double chamber microbial fuel cell was tested for the use of two cheap electrode materials copper and aluminum for the production of electricity under different operating conditions. The investigated conditions were concentration of microorganism (yeast) (0.5- 2 g/l), solutions temperature (33-45 ^oC) and concentration of glucose as a substrate (1.5- 6 g/l). The results demonstrated that copper electrode exhibit good performance while the performance of aluminum is poor. The electricity is generated with and without the addition of substrate. Addition of glucose substrate

The aim of this paper is to present the numerical method for solving linear system of Fredholm integral equations, based on the Haar wavelet approach. Many test problems, for which the exact solution is known, are considered. Compare the results of suggested method with the results of another method (Trapezoidal method). Algorithm and program is written by Matlab vergion 7.

Used vegetable oil was introduced to transesterfication reaction to produce Biodiesel fuel suitable for diesel engines. Method of production was consisted of filtration, transesterfication, separation and washing. Transesterfication was studied extensively with different operating conditions, temperature range (35-80oC), catalyst concentration (0.5-2 wt. % based on oil), mixing time (30-120 min.) with constant oil/methanol weight ratio 5:1 and mixing speed 1300 rpm. The concentration of Fatty acid methyl esters (Biodiesel) was determined for the transesterficated oil samples, besides of some important physical properties such as specific gravity, viscosity, pour point and flash point. The behavior of methyl esters production and the phys

Used vegetable oil was introduced to transesterfication reaction to produce Biodiesel fuel suitable for diesel engines. Method of production was consisted of filtration, transesterfication, separation and washing. Transesterfication was studied extensively with different operating conditions, temperature range (35-80o C), catalyst concentration (0.5-2 wt. % based on oil), mixing time (30-120 min.) with constant oil/methanol weight ratio 5:1 and mixing speed 1300 rpm. The concentration of Fatty acid methyl esters (Biodiesel) was determined for the transesterficated oil samples, besides of some important physical properties such as specific gravity, viscosity, pour point and flash point. The behavior of methyl esters production and the

Used vegetable oil was introduced to transesterfication reaction to produce Biodiesel fuel suitable for diesel engines. Method of production was consisted of filtration, transesterfication, separation and washing. Transesterfication was studied extensively with different operating conditions, temperature range (35-80oC), catalyst concentration (0.5-2 wt. % based on oil), mixing time (30-120 min.) with constant oil/methanol weight ratio 5:1 and mixing speed 1300 rpm. The concentration of Fatty acid methyl esters (Biodiesel) was determined for the transesterficated oil samples, besides of some important physical properties such as specific gravity, viscosity, pour point and flash point. The behavior of methyl esters production and the physica