This paper demonstrates a new technique based on a combined form of the new transform method with homotopy perturbation method to find the suitable accurate solution of autonomous Equations with initial condition.  This technique is called the transform homotopy perturbation method (THPM). It can be used to solve the problems without resorting to the frequency domain.The implementation of the suggested method demonstrates the usefulness in finding exact solution for linear and nonlinear problems. The practical results show the efficiency and reliability of technique and easier implemented than HPM in finding exact solutions.Finally, all algorithms in this paper implemented in MATLAB version 7.12.

The Hartley transform generalizes to the fractional Hartley transform (FRHT) which gives various uses in different fields of image encryption. Unfortunately, the available literature of fractional Hartley transform is unable to provide its inversion theorem. So accordingly original function cannot retrieve directly, which restrict its applications. The intension of this paper is to propose inversion theorem of fractional Hartley transform to overcome this drawback. Moreover, some properties of fractional Hartley transform are discussed in this paper.

A demonstration of the inverse kinematics is a very complex problem for redundant robot manipulator. This paper presents the solution of inverse kinematics for one of redundant robots manipulator (three link robot) by combing of two intelligent algorithms GA (Genetic Algorithm) and NN (Neural Network). The inputs are position and orientation of three link robot. These inputs are entering to Back Propagation Neural Network (BPNN). The weights of BPNN are optimized using continuous GA. The (Mean Square Error) MSE is also computed between the estimated and desired outputs of joint angles. In this paper, the fitness function in GA is proposed. The sinwave and circular for three link robot end effecter and desired trajectories are simulated b

Desalination is a process where fresh water produces from high salinity solutions, many ways used for this purpose and one of the most important processes is membrane distillation (MD). Direct contact membrane distillation (DCMD) can be considered as the most prominent type from MD types according to ease of design and modus operandi. This work studies the efficiency of using DCMD operation for desalination brine with different concentration (1.75, 3.5, 5 wt. % NaCl). Frame and plate cell was used with flat sheet PTFE hydrophobic type membrane. The study proves that MD is an effective process for desalination brines with feed temperature less than 60˚C especially for feed with low TDS. 37˚C, 47˚C, and 57˚C was feed t

The method of operational matrices based on different types of polynomials such as Bernstein, shifted Legendre and Bernoulli polynomials will be presented and implemented to solve the nonlinear Blasius equations approximately. The nonlinear differential equation will be converted into a system of nonlinear algebraic equations that can be solved using Mathematica^®12. The efficiency of these methods has been studied by calculating the maximum error remainder ( ), and it was found that their efficiency increases as the polynomial degree (n) increases, since the errors decrease. Moreover, the approximate solutions obtained by the proposed methods are compared with the solution of the 4^th order Runge-Kutta meth

The aim of this paper is to propose an efficient three steps iterative method for finding the zeros of the nonlinear equation f(x)=0 . Starting with a suitably chosen , the method generates a sequence of iterates converging to the root. The convergence analysis is proved to establish its five order of convergence. Several examples are given to illustrate the efficiency of the proposed new method and its comparison with other methods.