Adomian decomposition method

The phenomena of machine failures, defects, multiple rework loops, etc., results in much difficulty in modeling rework systems, and therefore the performance analysis of such systems has been investigated limitedly in the past. We propose an analytical method for the performance evaluation of rework systems with unreliable machines and finite buffers. To characterize the rework flow in the system, a new 3M1B (three-machine and one-buffer) Markov model is first presented. Unlike previous models, it is capable of representing multiple rework loops, and the rework fraction of each loop is calculated based on the quality of material flow in the system. A decomposition method is then developed for multistage rework systems using the proposed 3M1B model as one of the building blocks. The experimental results demonstrate that the decomposition method provides accurate estimates of performance measures such as throughput and Work-In-Process (WIP). We have applied this method to several problems, such as the determination of the optimal inspection location and the identification of bottleneck machines in rework systems.► We propose an analytical model for manufacturing systems with multiple rework loops. ► We solve problems such as inspection allocation and bottleneck identification. ► Bottlenecks of rework systems migrate differently compared to systems without rework. ► We propose a continuous improvement strategy in the paper.

... a Department of Basic Science, Benha Higher Institute of Technology, Benha University 13512, Egypt. b Department of Engineering Mathematics and Physics, Faculty of Engineering, CairoUniversity, Giza-Egypt. Received 1 March 2006; revised 3 May 2006. ...

Turbulent flow over a sinusoidal solid wavy surface was investigated by a direct numerical simulation using a spectral element technique. The train of waves has an amplitude to wavelength ratio of 0.05. For the flow conditions (Re=hU b/2ν= 3460) considered, adverse pressure gradients were large enough to cause flow separation. Numerical results compare favorably with those of Hudson's (1993) measurements. Instantaneous flow fields show a large variation of the flow pattern in the spanwise direction in the separated bubble at a given time. A surprising result is the discovery of occasional velocity bursts which originate in the separated region and extend over large distances away from the wavy wall. Turbulence in this region is very different from that near a flat wall in that it is associated with a shear layer which is formed by flow separation.

In this article we use Adomian decomposition method, which is a well-known method for solving functional equations now-a-days, to solve systems of differential equations of the first order and an ordinary differential equation of any order by converting it into a system of differential of the order one. Theoretical considerations are being discussed, and convergence of the method for theses systems is addressed. Some examples are presented to show the ability of the method for linear and non-linear systems of differential equations.

In this paper, we present a method to navigate a mobile robot using a webcam. This method determines the shortest path for the robot to transverse to its target location, while avoiding obstacles along the way. The environment is first captured as an image using a webcam. Image processing methods are then performed to identify the existence of obstacles within the environment. Using the Cell Decomposition method, locations with obstacles are identified and the corresponding cells are eliminated. From the remaining cells, the shortest path to the goal is identified. The program is written in MATLAB with the Image Processing toolbox. The proposed method does not make use of any other type of sensor other than the webcam.

The Lane-Emden equation describing temperature in a star in hydrostatic equilibrium was recently solved analytically by N.T. Shawagfeh [1] with highly accurate results using decomposition [1 9]. Further consideration suggests some computational advantage, avoidance of the initial transformations, possible generalizations in astrophysics, and a measurement to determine masses of the cepheids.

In this paper, a reliable algorithm is employed to investigate the differential equations of Lane–Emden type. The algorithm rests mainly on the Adomian decomposition method with an alternate framework designed to overcome the difficulty of the singular point. The proposed framework is applied to a generalization of Lane–Emden equations so that it can be used in differential equations of the same type.

The modified Laplace Adomian decomposition method (LADM) has been developed to find the analytic approximation solution of the nonlinear Volterra-Fredholm integro differential equations under the initial or boundary conditions. We prove the convergence of LADM applied to the Volterra-Fredholm integro differential equations. In this paper, some examples will be examined to support the proposed analysis.