Search results for: estimation method

Authors: M. S. Baazzim, M. S. Al-Saud, M. A. El-Kady

Abstract:

In this paper, steady-state ampacity (current carrying capacity) evaluation of underground power cable system by using analytical and numerical methods for different conditions (depth of cable, spacing between phases, soil thermal resistivity, ambient temperature, wind speed), for two system voltage level were used 132 and 380 kV. The analytical method or traditional method that was used is based on the thermal analysis method developed by Neher-McGrath and further enhanced by International Electrotechnical Commission (IEC) and published in standard IEC 60287. The numerical method that was used is finite element method and it was recourse commercial software based on finite element method. 

Keywords: Cable ampacity, Finite element method, underground cable, thermal rating.

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Authors: M. Saravi, F. Ashrafi, S.R. Mirrajei

Abstract:

As we know, most differential equations concerning physical phenomenon could not be solved by analytical method. Even if we use Series Method, some times we need an appropriate change of variable, and even when we can, their closed form solution may be so complicated that using it to obtain an image or to examine the structure of the system is impossible. For example, if we consider Schrodinger equation, i.e., We come to a three-term recursion relations, which work with it takes, at least, a little bit time to get a series solution[6]. For this reason we use a change of variable such as or when we consider the orbital angular momentum[1], it will be necessary to solve. As we can observe, working with this equation is tedious. In this paper, after introducing Clenshaw method, which is a kind of Spectral method, we try to solve some of such equations.

Keywords: Chebyshev polynomials, Clenshaw method, ODEs, Spectral methods

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Authors: A.Memari

Abstract:

In this article, a simulation method called the Homotopy Perturbation Method (HPM) is employed in the steady flow of a Walter's B' fluid in a vertical channel with porous wall. We employed Homotopy Perturbation Method to derive solution of a nonlinear form of equation obtained from exerting similarity transforming to the ordinary differential equation gained from continuity and momentum equations of this kind of flow. The results obtained from the Homotopy Perturbation Method are then compared with those from the Runge–Kutta method in order to verify the accuracy of the proposed method. The results show that the Homotopy Perturbation Method can achieve good results in predicting the solution of such problems. Ultimately we use this solution to obtain the other terms of velocities and physical discussion about it.

Keywords: Steady flow; Walter's B' Fluid;, vertical channel;porous media, Homotopy Perturbation Method (HPM), Numerical Solution (NS).

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Authors: S. Safi, M. Frikel, M. M'Saad, A. Zeroual

Abstract:

This paper describes a blind algorithm for estimating a time varying and frequency selective fading channel. In order to identify blindly the impulse response of these channels, we have used Higher Order Statistics (HOS) to build our algorithm. In this paper, we have selected two theoretical frequency selective channels as the Proakis-s 'B' channel and the Macchi-s channel, and one practical frequency selective fading channel called Broadband Radio Access Network (BRAN A). The simulation results in noisy environment and for different data input channel, demonstrate that the proposed method could estimate the phase and magnitude of these channels blindly and without any information about the input, except that the input excitation is i.i.d (Identically and Independent Distributed) and non-Gaussian.

Keywords: Frequency response, system identification, higher order statistics, communication channels, phase estimation.

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Authors: Ahmed G. Mahgoub, Dahlia H. Hafez, Mostafa A. Abu Kiefa

Abstract:

The Cone Penetration Test (CPT) is a common in-situ test which generally investigates a much greater volume of soil more quickly than possible from sampling and laboratory tests. Therefore, it has the potential to realize both cost savings and assessment of soil properties rapidly and continuously. The principle objective of this paper is to demonstrate the feasibility and efficiency of using artificial neural networks (ANNs) to predict the soil angle of internal friction (Φ) and the soil modulus of elasticity (E) from CPT results considering the uncertainties and non-linearities of the soil. In addition, ANNs are used to study the influence of different parameters and recommend which parameters should be included as input parameters to improve the prediction. Neural networks discover relationships in the input data sets through the iterative presentation of the data and intrinsic mapping characteristics of neural topologies. General Regression Neural Network (GRNN) is one of the powerful neural network architectures which is utilized in this study. A large amount of field and experimental data including CPT results, plate load tests, direct shear box, grain size distribution and calculated data of overburden pressure was obtained from a large project in the United Arab Emirates. This data was used for the training and the validation of the neural network. A comparison was made between the obtained results from the ANN's approach, and some common traditional correlations that predict Φ and E from CPT results with respect to the actual results of the collected data. The results show that the ANN is a very powerful tool. Very good agreement was obtained between estimated results from ANN and actual measured results with comparison to other correlations available in the literature. The study recommends some easily available parameters that should be included in the estimation of the soil properties to improve the prediction models. It is shown that the use of friction ration in the estimation of Φ and the use of fines content in the estimation of E considerable improve the prediction models.

Keywords: Angle of internal friction, Cone penetrating test, General regression neural network, Soil modulus of elasticity.

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Authors: Roman Graf, Sergiu Gordea, Heather M. Ryan

Abstract:

This paper presents an approach for the classification of an unstructured format description for identification of file formats. The main contribution of this work is the employment of data mining techniques to support file format selection with just the unstructured text description that comprises the most important format features for a particular organisation. Subsequently, the file format indentification method employs file format classifier and associated configurations to support digital preservation experts with an estimation of required file format. Our goal is to make use of a format specification knowledge base aggregated from a different Web sources in order to select file format for a particular institution. Using the naive Bayes method, the decision support system recommends to an expert, the file format for his institution. The proposed methods facilitate the selection of file format and the quality of a digital preservation process. The presented approach is meant to facilitate decision making for the preservation of digital content in libraries and archives using domain expert knowledge and specifications of file formats. To facilitate decision-making, the aggregated information about the file formats is presented as a file format vocabulary that comprises most common terms that are characteristic for all researched formats. The goal is to suggest a particular file format based on this vocabulary for analysis by an expert. The sample file format calculation and the calculation results including probabilities are presented in the evaluation section.

Keywords: Data mining, digital libraries, digital preservation, file format.

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Authors: Bharathi P. T, P. Subashini

Abstract:

Ice cover County has a significant impact on rivers as it affects with the ice melting capacity which results in flooding, restrict navigation, modify the ecosystem and microclimate. River ices are made up of different ice types with varying ice thickness, so surveillance of river ice plays an important role. River ice types are captured using infrared imaging camera which captures the images even during the night times. In this paper the river ice infrared texture images are analysed using first-order statistical methods and secondorder statistical methods. The second order statistical methods considered are spatial gray level dependence method, gray level run length method and gray level difference method. The performance of the feature extraction methods are evaluated by using Probabilistic Neural Network classifier and it is found that the first-order statistical method and second-order statistical method yields low accuracy. So the features extracted from the first-order statistical method and second-order statistical method are combined and it is observed that the result of these combined features (First order statistical method + gray level run length method) provides higher accuracy when compared with the features from the first-order statistical method and second-order statistical method alone.

Keywords: Gray Level Difference Method, Gray Level Run Length Method, Kurtosis, Probabilistic Neural Network, Skewness, Spatial Gray Level Dependence Method.

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Authors: Marwa I. Shabayek, Ola A. Said, Hanan A. Attaia, Heba A. Awida

Abstract:

Bladder carcinoma is an important worldwide health problem. Both cystoscopy and urine cytology used in detecting bladder cancer suffer from drawbacks where cystoscopy is an invasive method and urine cytology shows low sensitivity in low grade tumors. This study validates easier and less time-consuming techniques to evaluate the value of combined use of angiogenin and clusterin in comparison and combination with voided urine cytology in the detection of bladder cancer patients. This study includes malignant (bladder cancer patients, n= 50), benign (n=20) and healthy (n=20) groups. The studied groups were subjected to cystoscopic examination, detection of bilharzial antibodies, urine cytology, and estimation of urinary angiogenin and clusterin by ELISA. The overall sensitivity and specificity were 66% and 75% for angiogenin, 70% and 82.5% for clusterin and 46% and 80% for voided urine cytology. Combined sensitivity of angiogenin and clusterin with urine cytology increased from 82 to 88%. 

Keywords: Angiogenin, Bladder Cancer, Clusterin, Cytology.

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Authors: Sunyoung Bu, Wonkyu Chung, Philsu Kim

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In this paper, we introduce a method for improving the embedded Runge-Kutta-Fehlberg4(5) method. At each integration step, the proposed method is comprised of two equations for the solution and the error, respectively. These solution and error are obtained by solving an initial value problem whose solution has the information of the error at each integration step. The constructed algorithm controls both the error and the time step size simultaneously and possesses a good performance in the computational cost compared to the original method. For the assessment of the effectiveness, EULR problem is numerically solved.

Keywords: Embedded Runge-Kutta-Fehlberg method, Initial value problem.

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Authors: Saheed A. Gbadegeshin

Abstract:

Commercialization method is a means to make inventions available at the market for final consumption. It is described as an important tool for keeping business enterprises sustainable and improving national economic growth. Thus, there are several scholarly publications on it, either presenting or testing different methods for commercialization. However, young entrepreneurs, technologists and scientists would like to know the best method to commercialize their innovations. Then, this question arises: What is the best commercialization method? To answer the question, a systematic literature review was conducted, and practitioners were interviewed. The literary results revealed that there are many methods but new methods are needed to improve commercialization especially during these times of economic crisis and political uncertainty. Similarly, the empirical results showed there are several methods, but the best method is the one that reduces costs, reduces the risks associated with uncertainty, and improves customer participation and acceptability. Therefore, it was concluded that new commercialization method is essential for today's high technologies and a method was presented.

Keywords: Commercialization method, high technology, lean start-up methodology, technology, knowledge.

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Authors: N. L. S. Ahmad, Y. L. Thong, P. Nambiar

Abstract:

An in vitro study was carried out to evaluate the feasibility of small field of view (FOV) cone beam computed tomography (CBCT) in determining endodontic working length. The objectives were to determine the accuracy of CBCT in measuring the estimated preoperative working lengths (EPWL), endodontic working lengths (EWL) and file lengths. Access cavities were prepared in 27 molars. For each root canal, the baseline electronic working length was determined using an EAL (Raypex 5). The teeth were then divided into overextended, non-modified and underextended groups and the lengths were adjusted accordingly. Imaging and measurements were made using the respective software of the RVG (Kodak RVG 6100) and CBCT units (Kodak 9000 3D). Root apices were then shaved and the apical constrictions viewed under magnification to measure the control working lengths. The paired t-test showed a statistically significant difference between CBCT EPWL and control length but the difference was too small to be clinically significant. From the Bland Altman analysis, the CBCT method had the widest range of 95% limits of agreement, reflecting its greater potential of error. In measuring file lengths, RVG had a bigger window of 95% limits of agreement compared to CBCT. Conclusions: (1) The clinically insignificant underestimation of the preoperative working length using small FOV CBCT showed that it is acceptable for use in the estimation of preoperative working length. (2) Small FOV CBCT may be used in working length determination but it is not as accurate as the currently practiced method of using the EAL. (3) It is also more accurate than RVG in measuring file lengths.

Keywords: Accuracy, CBCT, endodontic, measurement.

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Authors: Li Hao, Yan Zhang, Jingan Cui

Abstract:

The Eulerian numerical method is proposed to analyze the explosion in tunnel. Based on this method, an original software M-MMIC2D is developed by Cµ program language. With this software, the explosion problem in the tunnel with three expansion-chambers is numerically simulated, and the results are found to be in full agreement with the observed experimental data.

Keywords: Eulerian method, numerical simulation, shock wave, tunnel

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Authors: Rafic Ayoubi, Jean-Pierre Dubois, Rania Minkara

Abstract:

In this paper, we study FPGA implementation of a novel supra-optimal receiver diversity combining technique, generalized maximal ratio combining (GMRC), for wireless transmission over fading channels in SIMO systems. Prior published results using ML-detected GMRC diversity signal driven by BPSK showed superior bit error rate performance to the widely used MRC combining scheme in an imperfect channel estimation (ICE) environment. Under perfect channel estimation conditions, the performance of GMRC and MRC were identical. The main drawback of the GMRC study was that it was theoretical, thus successful FPGA implementation of it using pipeline techniques is needed as a wireless communication test-bed for practical real-life situations. Simulation results showed that the hardware implementation was efficient both in terms of speed and area. Since diversity combining is especially effective in small femto- and picocells, internet-associated wireless peripheral systems are to benefit most from GMRC. As a result, many spinoff applications can be made to the hardware of IP-based 4th generation networks.

Keywords: Femto-internet cells, field-programmable gate array, generalized maximal-ratio combining, Lyapunov fractal dimension, pipelining technique, wireless SIMO channels.

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Authors: Amit Kumar, Anila Gupta, Amarpreet Kaur

Abstract:

In this paper, a new method is proposed to find the fuzzy optimal solution of fuzzy assignment problems by representing all the parameters as triangular fuzzy numbers. The advantages of the pro-posed method are also discussed. To illustrate the proposed method a fuzzy assignment problem is solved by using the proposed method and the obtained results are discussed. The proposed method is easy to understand and to apply for finding the fuzzy optimal solution of fuzzy assignment problems occurring in real life situations.

Keywords: Fuzzy assignment problem, Ranking function, Triangular fuzzy numbers.

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Authors: Mohammad A. Khasawneh

Abstract:

Asphalt concrete pavements gradually lose their skid resistance causing safety problems especially under wet conditions and high driving speeds. In order to enact the actual field polishing and wearing process of asphalt pavement surfaces in a laboratory setting, several laboratory-scale accelerated polishing devices were developed by different agencies. To mimic the actual process, friction and texture measuring devices are needed to quantify surface deterioration at different polishing intervals that reflect different stages of the pavement life. The test could still be considered lengthy and to some extent labor-intensive. Therefore, there is a need to come up with another method that can assist in investigating the bituminous pavement surface characteristics in a practical and time-efficient test procedure.

The purpose of this paper is to utilize a well-developed image analysis technique to characterize asphalt pavement surfaces without the need to use conventional friction and texture measuring devices in an attempt to shorten and simplify the polishing procedure in the lab.

Promising findings showed the possibility of using image analysis in lieu of the labor-sensitive-variable-in-nature friction and texture measurements. It was found that the exposed aggregate surface area of asphalt specimens made from limestone and gravel aggregates produced solid evidence of the validity of this method in describing asphalt pavement surfaces. Image analysis results correlated well with the British Pendulum Numbers (BPN), Polish Values (PV) and Mean Texture Depth (MTD) values.

Keywords: Friction, Image Analysis, Polishing, Statistical Analysis, Texture.

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Authors: Haijie Li, Xuping Zhang

Abstract:

This paper presents a computationally efficient method for the modeling of robot manipulators with flexible links and joints. This approach combines the Discrete Time Transfer Matrix Method with the Finite Segment Method, in which the flexible links are discretized by a number of rigid segments connected by torsion springs; and the flexibility of joints are modeled by torsion springs. The proposed method avoids the global dynamics and has the advantage of modeling non-uniform manipulators. Experiments and simulations of a single-link flexible manipulator are conducted for verifying the proposed methodologies. The simulations of a three-link robot arm with links and joints flexibility are also performed.

Keywords: Flexible manipulator, transfer matrix method, linearization, finite segment method.

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Authors: Axay J Mehta, Hema A Mehta, T.C.Manjunath, C. Ardil

Abstract:

In this paper, the modelling and design of artificial neural network architecture for load forecasting purposes is investigated. The primary pre-requisite for power system planning is to arrive at realistic estimates of future demand of power, which is known as Load Forecasting. Short Term Load Forecasting (STLF) helps in determining the economic, reliable and secure operating strategies for power system. The dependence of load on several factors makes the load forecasting a very challenging job. An over estimation of the load may cause premature investment and unnecessary blocking of the capital where as under estimation of load may result in shortage of equipment and circuits. It is always better to plan the system for the load slightly higher than expected one so that no exigency may arise. In this paper, a load-forecasting model is proposed using a multilayer neural network with an appropriately modified back propagation learning algorithm. Once the neural network model is designed and trained, it can forecast the load of the power system 24 hours ahead on daily basis and can also forecast the cumulative load on daily basis. The real load data that is used for the Artificial Neural Network training was taken from LDC, Gujarat Electricity Board, Jambuva, Gujarat, India. The results show that the load forecasting of the ANN model follows the actual load pattern more accurately throughout the forecasted period.

Keywords: Power system, Load forecasting, Neural Network, Neuron, Stabilization, Network structure, Load.

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Authors: S. N. Hosseini, S. M. H. Karimian

Abstract:

A new conserving approach in the context of Immersed Boundary Method (IBM) is presented to simulate one dimensional, incompressible flow in a moving boundary problem. The method employs control volume scheme to simulate the flow field. The concept of ghost node is used at the boundaries to conserve the mass and momentum equations. The Present method implements the conservation laws in all cells including boundary control volumes. Application of the method is studied in a test case with moving boundary. Comparison between the results of this new method and a sharp interface (Image Point Method) IBM algorithm shows a well distinguished improvement in both pressure and velocity fields of the present method. Fluctuations in pressure field are fully resolved in this proposed method. This approach expands the IBM capability to simulate flow field for variety of problems by implementing conservation laws in a fully Cartesian grid compared to other conserving methods.

Keywords: Immersed Boundary Method, conservation of mass and momentum laws, moving boundary, boundary condition.

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Authors: Wei Zhang, Hong Yu, Xian-ping Zhao, Da-da Wang, Fei Xue

Abstract:

For lack of the visualization of the ultrasonic detection method of partial discharge (PD), the ultrasonic detection technology combined with the X-ray visual detection method (UXV) is proposed. The method can conduct qualitative analysis accurately and conduct reliable positioning diagnosis to the internal insulation defects of GIS, and while it could make up the blindness of the X-ray visual detection method and improve the detection rate. In this paper, an experimental model of GIS is used as the trial platform, a variety of insulation defects are set inside the GIS cavity. With the proposed method, the ultrasonic method is used to conduct the preliminary detection, and then the X-ray visual detection is used to locate and diagnose precisely. Therefore, the proposed UXV technology is feasible and practical.

Keywords: GIS, ultrasonic, visual detection, X-ray

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Authors: M. Zarebnia, R. Parvaz

Abstract:

In this paper the Kuramoto-Sivashinsky equation is solved numerically by collocation method. The solution is approximated as a linear combination of septic B-spline functions. Applying the Von-Neumann stability analysis technique, we show that the method is unconditionally stable. The method is applied on some test examples, and the numerical results have been compared with the exact solutions. The global relative error and L∞ in the solutions show the efficiency of the method computationally.

Keywords: Kuramoto-Sivashinsky equation, Septic B-spline, Collocation method, Finite difference.

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Authors: Yanan Yang, Zhigang Wang, Xiang Chen

Abstract:

This paper presents the use of Legendre pseudospectral method for the optimization of finite-thrust orbital transfer for spacecrafts. In order to get an accurate solution, the System-s dynamics equations were normalized through a dimensionless method. The Legendre pseudospectral method is based on interpolating functions on Legendre-Gauss-Lobatto (LGL) quadrature nodes. This is used to transform the optimal control problem into a constrained parameter optimization problem. The developed novel optimization algorithm can be used to solve similar optimization problems of spacecraft finite-thrust orbital transfer. The results of a numerical simulation verified the validity of the proposed optimization method. The simulation results reveal that pseudospectral optimization method is a promising method for real-time trajectory optimization and provides good accuracy and fast convergence.

Keywords: Finite-thrust, Orbital transfer, Legendre pseudospectral method

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Authors: Hailong Zhu, Zhaoxiang Li, Kejun Zhuang

Abstract:

By means of Contractor Iteration Method, we solve and visualize the Lane-Emden(-Fowler) equation Δu + up = 0, in Ω, u = 0, on ∂Ω. It is shown that the present method converges quadratically as Newton’s method and the computation of Contractor Iteration Method is cheaper than the Newton’s method.

Keywords: Positive solutions, newton's method, contractor iteration method, Eigenpairs.

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Authors: Osamu Igawa, Hiroshi Kouchiwa, Yuji Ito

Abstract:

In recent years, a reconstruction project for sewer  pipelines has been progressing in Japan with the aim of renewing old  sewer culverts. However, it is difficult to secure a sufficient base area  for shafts in an urban area because many streets are narrow with a  complex layout. As a result, construction in such urban areas is  generally very demanding.  In urban areas, there is a strong requirement for a safe, reliable and  economical construction method that does not disturb the public’s  daily life and urban activities. With this in mind, we developed a new  construction method called the “shield switching type micro-tunneling  method,” which integrates the micro-tunneling method and shield  method.  In this method, pipeline is constructed first for sections that are  gently curved or straight using the economical micro-tunneling  method, and then the method is switched to the shield method for  sections with a sharp curve or a series of curves without establishing  an intermediate shaft.  This paper provides the information, features and construction  examples of this newly developed method.

 

Keywords: Micro-tunneling method, Secondary lining applied RC segment, Sharp curve, Shield method, Switching type.

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Authors: Shigeaki Sakurai, Ryohei Orihara

Abstract:

This paper proposes a new method for analyzing textual data. The method deals with items of textual data, where each item is described based on various viewpoints. The method acquires 2- class classification models of the viewpoints by applying an inductive learning method to items with multiple viewpoints. The method infers whether the viewpoints are assigned to the new items or not by using the models. The method extracts expressions from the new items classified into the viewpoints and extracts characteristic expressions corresponding to the viewpoints by comparing the frequency of expressions among the viewpoints. This paper also applies the method to questionnaire data given by guests at a hotel and verifies its effect through numerical experiments.

Keywords: Text mining, Multiple viewpoints, Differential analysis, Questionnaire data

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Authors: Mahmoud Zarrini

Abstract:

Avalanche release of snow has been modeled in the present studies. Snow is assumed to be represented by semi-solid and the governing equations have been studied from the concept of continuum approach. The dynamical equations have been solved for two different zones [starting zone and track zone] by using appropriate initial and boundary conditions. Effect of density (ρ), Eddy viscosity (η), Slope angle (θ), Slab depth (R) on the flow parameters have been observed in the present studies. Numerical methods have been employed for computing the non linear differential equations. One of the most interesting and fundamental innovation in the present studies is getting initial condition for the computation of velocity by numerical approach. This information of the velocity has obtained through the concept of fracture mechanics applicable to snow. The results on the flow parameters have found to be in qualitative agreement with the published results.

Keywords: Snow avalanche, fracture mechanics, avalanche velocity, avalanche zones.

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Authors: A. Raminfard, S. M. Shahrtash

Abstract:

In this paper, a new efficient method for load balancing in low voltage distribution systems is presented. The proposed method introduces an improved Leap-frog method for optimization. The proposed objective function includes the difference between three phase currents, as well as two other terms to provide the integer property of the variables; where the latter are the status of the connection of loads to different phases. Afterwards, a new algorithm is supplemented to undertake the integer values for the load connection status. Finally, the method is applied to different parts of Tabriz low voltage network, where the results have shown the good performance of the proposed method.

Keywords: Load balancing, improved leap-frog method, optimization algorithm, low voltage distribution systems.

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Authors: Parvinder S. Sandhu, Manisha Prashar, Pourush Bassi, Atul Bisht

Abstract:

Software effort estimation is the process of predicting the most realistic use of effort required to develop or maintain software based on incomplete, uncertain and/or noisy input. Effort estimates may be used as input to project plans, iteration plans, budgets. There are various models like Halstead, Walston-Felix, Bailey-Basili, Doty and GA Based models which have already used to estimate the software effort for projects. In this study Statistical Models, Fuzzy-GA and Neuro-Fuzzy (NF) Inference Systems are experimented to estimate the software effort for projects. The performances of the developed models were tested on NASA software project datasets and results are compared with the Halstead, Walston-Felix, Bailey-Basili, Doty and Genetic Algorithm Based models mentioned in the literature. The result shows that the NF Model has the lowest MMRE and RMSE values. The NF Model shows the best results as compared with the Fuzzy-GA based hybrid Inference System and other existing Models that are being used for the Effort Prediction with lowest MMRE and RMSE values.

Keywords: Neuro-Fuzzy Model, Halstead Model, Walston-Felix Model, Bailey-Basili Model, Doty Model, GA Based Model, Genetic Algorithm.

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Authors: Changqing Yang, Jianhua Hou, Beibo Qin

Abstract:

A numerical method for Riccati equation is presented in this work. The method is based on the replacement of unknown functions through a truncated series of hybrid of block-pulse functions and Chebyshev polynomials. The operational matrices of derivative and product of hybrid functions are presented. These matrices together with the tau method are then utilized to transform the differential equation into a system of algebraic equations. Corresponding numerical examples are presented to demonstrate the accuracy of the proposed method.

Keywords: Hybrid functions, Riccati differential equation, Blockpulse, Chebyshev polynomials, Tau method, operational matrix.

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Authors: Lina Yan, Shiheng Wang, Ke Wang

Abstract:

A preconditioned Jacobi (PJ) method is provided for solving fuzzy linear systems whose coefficient matrices are crisp Mmatrices and the right-hand side columns are arbitrary fuzzy number vectors. The iterative algorithm is given for the preconditioned Jacobi method. The convergence is analyzed with convergence theorems. Numerical examples are given to illustrate the procedure and show the effectiveness and efficiency of the method.

Keywords: preconditioning, M-matrix, Jacobi method, fuzzy linear system (FLS).

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Authors: H. N. Agiza, M. A. Sohaly, M. A. Elfouly

Abstract:

Parkinson's disease (PD) is a heterogeneous disorder with common age of onset, symptoms, and progression levels. In this paper we will solve analytically the PD model as a non-linear delay differential equation using the steps method. The step method transforms a system of delay differential equations (DDEs) into systems of ordinary differential equations (ODEs). On some numerical examples, the analytical solution will be difficult. So we will approximate the analytical solution using Picard method and Taylor method to ODEs.

Keywords: Parkinson's disease, Step method, delay differential equation, simulation.

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