Search results for: Fast Decoupled method
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 8608

Search results for: Fast Decoupled method

8248 A Dual Method for Solving General Convex Quadratic Programs

Authors: Belkacem Brahmi, Mohand Ouamer Bibi

Abstract:

In this paper, we present a new method for solving quadratic programming problems, not strictly convex. Constraints of the problem are linear equalities and inequalities, with bounded variables. The suggested method combines the active-set strategies and support methods. The algorithm of the method and numerical experiments are presented, while comparing our approach with the active set method on randomly generated problems.

Keywords: Convex quadratic programming, dual support methods, active set methods.

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8247 Zero-Dissipative Explicit Runge-Kutta Method for Periodic Initial Value Problems

Authors: N. Senu, I. A. Kasim, F. Ismail, N. Bachok

Abstract:

In this paper zero-dissipative explicit Runge-Kutta method is derived for solving second-order ordinary differential equations with periodical solutions. The phase-lag and dissipation properties for Runge-Kutta (RK) method are also discussed. The new method has algebraic order three with dissipation of order infinity. The numerical results for the new method are compared with existing method when solving the second-order differential equations with periodic solutions using constant step size.

Keywords: Dissipation, Oscillatory solutions, Phase-lag, Runge- Kutta methods.

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8246 Selection Initial modes for Belief K-modes Method

Authors: Sarra Ben Hariz, Zied Elouedi, Khaled Mellouli

Abstract:

The belief K-modes method (BKM) approach is a new clustering technique handling uncertainty in the attribute values of objects in both the cluster construction task and the classification one. Like the standard version of this method, the BKM results depend on the chosen initial modes. So, one selection method of initial modes is developed, in this paper, aiming at improving the performances of the BKM approach. Experiments with several sets of real data show that by considered the developed selection initial modes method, the clustering algorithm produces more accurate results.

Keywords: Clustering, Uncertainty, Belief function theory, Belief K-modes Method, Initial modes selection.

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8245 Variational Iteration Method for Solving Systems of Linear Delay Differential Equations

Authors: Sara Barati, Karim Ivaz

Abstract:

In this paper, using a model transformation approach a system of linear delay differential equations (DDEs) with multiple delays is converted to a non-delayed initial value problem. The variational iteration method (VIM) is then applied to obtain the approximate analytical solutions. Numerical results are given for several examples involving scalar and second order systems. Comparisons with the classical fourth-order Runge-Kutta method (RK4) verify that this method is very effective and convenient.

Keywords: Variational iteration method, delay differential equations, multiple delays, Runge-Kutta method.

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8244 Comparison of Finite-Element and IEC Methods for Cable Thermal Analysis under Various Operating Environments

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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8243 Numerical Solution of Linear Ordinary Differential Equations in Quantum Chemistry by Clenshaw Method

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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8242 Application of Homotopy Perturbation Method to Solve Steady Flow of Walter B Fluid A Vertical Channel In Porous Media

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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8241 Graph Codes-2D Projections of Multimedia Feature Graphs for Fast and Effective Retrieval

Authors: Stefan Wagenpfeil, Felix Engel, Paul McKevitt, Matthias Hemmje

Abstract:

Multimedia Indexing and Retrieval is generally de-signed and implemented by employing feature graphs. These graphs typically contain a significant number of nodes and edges to reflect the level of detail in feature detection. A higher level of detail increases the effectiveness of the results but also leads to more complex graph structures. However, graph-traversal-based algorithms for similarity are quite inefficient and computation intensive, espe-cially for large data structures. To deliver fast and effective retrieval, an efficient similarity algorithm, particularly for large graphs, is mandatory. Hence, in this paper, we define a graph-projection into a 2D space (Graph Code) as well as the corresponding algorithms for indexing and retrieval. We show that calculations in this space can be performed more efficiently than graph-traversals due to a simpler processing model and a high level of parallelisation. In consequence, we prove that the effectiveness of retrieval also increases substantially, as Graph Codes facilitate more levels of detail in feature fusion. Thus, Graph Codes provide a significant increase in efficiency and effectiveness (especially for Multimedia indexing and retrieval) and can be applied to images, videos, audio, and text information.

Keywords: indexing, retrieval, multimedia, graph code, graph algorithm

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8240 Texture Feature Extraction of Infrared River Ice Images using Second-Order Spatial Statistics

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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8239 A Method for Improving the Embedded Runge Kutta Fehlberg 4(5)

Authors: Sunyoung Bu, Wonkyu Chung, Philsu Kim

Abstract:

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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8238 Stating Best Commercialization Method: An Unanswered Question from Scholars and Practitioners

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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8237 Design of QFT-Based Self-Tuning Deadbeat Controller

Authors: H. Mansor, S. B. Mohd Noor

Abstract:

This paper presents a design method of self-tuning Quantitative Feedback Theory (QFT) by using improved deadbeat control algorithm. QFT is a technique to achieve robust control with pre-defined specifications whereas deadbeat is an algorithm that could bring the output to steady state with minimum step size. Nevertheless, usually there are large peaks in the deadbeat response. By integrating QFT specifications into deadbeat algorithm, the large peaks could be tolerated. On the other hand, emerging QFT with adaptive element will produce a robust controller with wider coverage of uncertainty. By combining QFT-based deadbeat algorithm and adaptive element, superior controller that is called selftuning QFT-based deadbeat controller could be achieved. The output response that is fast, robust and adaptive is expected. Using a grain dryer plant model as a pilot case-study, the performance of the proposed method has been evaluated and analyzed. Grain drying process is very complex with highly nonlinear behaviour, long delay, affected by environmental changes and affected by disturbances. Performance comparisons have been performed between the proposed self-tuning QFT-based deadbeat, standard QFT and standard dead-beat controllers. The efficiency of the self-tuning QFTbased dead-beat controller has been proven from the tests results in terms of controller’s parameters are updated online, less percentage of overshoot and settling time especially when there are variations in the plant.

Keywords: Deadbeat control, quantitative feedback theory (QFT), robust control, self-tuning control.

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8236 An Eulerian Numerical Method and its Application to Explosion Problems

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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8235 Method for Solving Fully Fuzzy Assignment Problems Using Triangular Fuzzy Numbers

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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8234 High Resolution Methods Based On Rank Revealing Triangular Factorizations

Authors: M. Bouri, S. Bourennane

Abstract:

In this paper, we propose a novel method for subspace estimation used high resolution method without eigendecomposition where the sample Cross-Spectral Matrix (CSM) is replaced by upper triangular matrix obtained from LU factorization. This novel method decreases the computational complexity. The method relies on a recently published result on Rank-Revealing LU (RRLU) factorization. Simulation results demonstrates that the new algorithm outperform the Householder rank-revealing QR (RRQR) factorization method and the MUSIC in the low Signal to Noise Ratio (SNR) scenarios.

Keywords: Factorization, Localization, Matrix, Signalsubspace.

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8233 A Method for Modeling Flexible Manipulators: Transfer Matrix Method with Finite Segments

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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8232 Application of Novel Conserving Immersed Boundary Method to Moving Boundary Problem

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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8231 Improvement of Model for SIMMER Code for SFR Corium Relocation Studies

Authors: A. Bachrata, N. Marie, F. Bertrand, J. B. Droin

Abstract:

The in-depth understanding of severe accident propagation in Generation IV of nuclear reactors is important so that appropriate risk management can be undertaken early in their design process. This paper is focused on model improvements in the SIMMER code in order to perform studies of severe accident mitigation of Sodium Fast Reactor. During the design process of the mitigation devices dedicated to extraction of molten fuel from the core region, the molten fuel propagation from the core up to the core catcher has to be studied. In this aim, analytical as well as the complex thermohydraulic simulations with SIMMER-III code are performed. The studies presented in this paper focus on physical phenomena and associated physical models that influence the corium relocation. Firstly, the molten pool heat exchange with surrounding structures is analyzed since it influences directly the instant of rupture of the dedicated tubes favoring the corium relocation for mitigation purpose. After the corium penetration into mitigation tubes, the fuel-coolant interactions result in formation of debris bed. Analyses of debris bed fluidization as well as sinking into a fluid are presented in this paper.

Keywords: Corium, mitigation tubes, SIMMER-III, sodium fast reactor (SFR).

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8230 The Comprehensive Study Based on Ultrasonic and X-ray Visual Technology for GIS Equipment Detection

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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8229 Septic B-Spline Collocation Method for Numerical Solution of the Kuramoto-Sivashinsky Equation

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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8228 Fuzzy Logic Controlled Shunt Active Power Filter for Three-phase Four-wire Systems with Balanced and Unbalanced Loads

Authors: Ahmed A. Helal, Nahla E. Zakzouk, Yasser G. Desouky

Abstract:

This paper presents a fuzzy logic controlled shunt active power filter used to compensate for harmonic distortion in three-phase four-wire systems. The shunt active filter employs a simple method for the calculation of the reference compensation current based of Fast Fourier Transform. This presented filter is able to operate in both balanced and unbalanced load conditions. A fuzzy logic based current controller strategy is used to regulate the filter current and hence ensure harmonic free supply current. The validity of the presented approach in harmonic mitigation is verified via simulation results of the proposed test system under different loading conditions.

Keywords: Active power filters, Fuzzy logic controller, Power quality

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8227 A State Aggregation Approach to Singularly Perturbed Markov Reward Processes

Authors: Dali Zhang, Baoqun Yin, Hongsheng Xi

Abstract:

In this paper, we propose a single sample path based algorithm with state aggregation to optimize the average rewards of singularly perturbed Markov reward processes (SPMRPs) with a large scale state spaces. It is assumed that such a reward process depend on a set of parameters. Differing from the other kinds of Markov chain, SPMRPs have their own hierarchical structure. Based on this special structure, our algorithm can alleviate the load in the optimization for performance. Moreover, our method can be applied on line because of its evolution with the sample path simulated. Compared with the original algorithm applied on these problems of general MRPs, a new gradient formula for average reward performance metric in SPMRPs is brought in, which will be proved in Appendix, and then based on these gradients, the schedule of the iteration algorithm is presented, which is based on a single sample path, and eventually a special case in which parameters only dominate the disturbance matrices will be analyzed, and a precise comparison with be displayed between our algorithm with the old ones which is aim to solve these problems in general Markov reward processes. When applied in SPMRPs, our method will approach a fast pace in these cases. Furthermore, to illustrate the practical value of SPMRPs, a simple example in multiple programming in computer systems will be listed and simulated. Corresponding to some practical model, physical meanings of SPMRPs in networks of queues will be clarified.

Keywords: Singularly perturbed Markov processes, Gradient of average reward, Differential reward, State aggregation, Perturbed close network.

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8226 A Contractor Iteration Method Using Eigenpairs for Positive Solutions of Nonlinear Elliptic Equation

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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8225 Sewer Culvert Installation Method to Accommodate Underground Construction in an Urban Area with Narrow Streets (The Development of Shield Switching Type Micro-Tunneling Method and the Introduction of Construction Examples)

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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8224 Analysis of Textual Data Based On Multiple 2-Class Classification Models

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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8223 A Practical Method for Load Balancing in the LV Distribution Networks Case Study: Tabriz Electrical Network

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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8222 A Novel Hopfield Neural Network for Perfect Calculation of Magnetic Resonance Spectroscopy

Authors: Hazem M. El-Bakry

Abstract:

In this paper, an automatic determination algorithm for nuclear magnetic resonance (NMR) spectra of the metabolites in the living body by magnetic resonance spectroscopy (MRS) without human intervention or complicated calculations is presented. In such method, the problem of NMR spectrum determination is transformed into the determination of the parameters of a mathematical model of the NMR signal. To calculate these parameters efficiently, a new model called modified Hopfield neural network is designed. The main achievement of this paper over the work in literature [30] is that the speed of the modified Hopfield neural network is accelerated. This is done by applying cross correlation in the frequency domain between the input values and the input weights. The modified Hopfield neural network can accomplish complex dignals perfectly with out any additinal computation steps. This is a valuable advantage as NMR signals are complex-valued. In addition, a technique called “modified sequential extension of section (MSES)" that takes into account the damping rate of the NMR signal is developed to be faster than that presented in [30]. Simulation results show that the calculation precision of the spectrum improves when MSES is used along with the neural network. Furthermore, MSES is found to reduce the local minimum problem in Hopfield neural networks. Moreover, the performance of the proposed method is evaluated and there is no effect on the performance of calculations when using the modified Hopfield neural networks.

Keywords: Hopfield Neural Networks, Cross Correlation, Nuclear Magnetic Resonance, Magnetic Resonance Spectroscopy, Fast Fourier Transform.

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8221 Numerical Solution of Riccati Differential Equations by Using Hybrid Functions and Tau Method

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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8220 Preconditioned Jacobi Method for Fuzzy Linear Systems

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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8219 Step Method for Solving Nonlinear Two Delays Differential Equation in Parkinson’s Disease

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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