Problem solving methods and mechanisms contribute to facilitating human life by providing tools to solve simple and complex daily problems. These mechanisms have been essential tools for professional designers and design students in solving design problems.
This research dealt with one of those mechanisms, which is the (the substance-field model model), as it has been mentioning that this mechanism is characterized by the difficulty of its application, which formed the main research problem. In home gardens (the sub-problem of research), an analysis of this problem was applied and then a solution was found to address it. The researcher used the 3dsmax program to implement the proposed design.
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in this paper the collocation method will be solve ordinary differential equations of retarted arguments also some examples are presented in order to illustrate this approach

In this paper, we have been used the Hermite interpolation method to solve second order regular boundary value problems for singular ordinary differential equations. The suggest method applied after divided the domain into many subdomains then used Hermite interpolation on each subdomain, the solution of the equation is equal to summation of the solution in each subdomain. Finally, we gave many examples to illustrate the suggested method and its efficiency.

In this Paper, we proposed two new predictor corrector methods for solving Kepler's equation in hyperbolic case using quadrature formula which plays an important and significant rule in the evaluation of the integrals. The two procedures are developed that, in two or three iterations, solve the hyperbolic orbit equation in a very efficient manner, and to an accuracy that proves to be always better than 10-15. The solution is examined with and with grid size , using the first guesses hyperbolic eccentric anomaly is and , where is the eccentricity and is the hyperbolic mean anomaly.

Abstract 

This paper presents an intelligent model reference adaptive control (MRAC) utilizing a self-recurrent wavelet neural network (SRWNN) to control nonlinear systems. The proposed SRWNN is an improved version of a previously reported wavelet neural network (WNN). In particular, this improvement was achieved by adopting two modifications to the original WNN structure. These modifications include, firstly, the utilization of a specific initialization phase to improve the convergence to the optimal weight values, and secondly, the inclusion of self-feedback weights to the wavelons of the wavelet layer. Furthermore, an on-line training procedure was proposed to enhance the control per

In the present work, a z-scan technique was used to study the nonlinear optical properties, represented by the nonlinear refractive index and nonlinear absorption coefficients of nanoparticles cadmium sulfide thin film. The sample was prepared by the chemical bath deposition method. Several testing were done including, x-ray, transmission and thickness of thin film. z-Scan experiment was performed at two wavelengths (1064 nm and 532 nm) and different energies. The results showed the effect of self-focusing in the material at higher intensities, which evaluated n2 to be (0.11-0.16) cm2/GW. The effect of two-photon absorption was studied, which evaluated β to be (24-106) cm/GW. In addition, the optical limiting behavior has been studied.

This paper presents a cognition path planning with control algorithm design for a nonholonomic wheeled mobile robot based on Particle Swarm Optimization (PSO) algorithm. The aim of this work is to propose the circular roadmap (CRM) method to plan and generate optimal path with free navigation as well as to propose a nonlinear MIMO-PID-MENN controller in order to track the wheeled mobile robot on the reference path. The PSO is used to find an online tune the control parameters of the proposed controller to get the best torques actions for the wheeled mobile robot. The numerical simulation results based on the Matlab package show that the proposed structure has a precise and highly accurate distance of the generated refere