Search results for: discrete choice models
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 3403

Search results for: discrete choice models

3253 The Effect of Particle Porosity in Mixed Matrix Membrane Permeation Models

Authors: Z. Sadeghi, M. R. Omidkhah, M. E. Masoomi

Abstract:

The purpose of this paper is to examine gas transport behavior of mixed matrix membranes (MMMs) combined with porous particles. Main existing models are categorized in two main groups; two-phase (ideal contact) and three-phase (non-ideal contact). A new coefficient, J, was obtained to express equations for estimating effect of the particle porosity in two-phase and three-phase models. Modified models evaluates with existing models and experimental data using Matlab software. Comparison of gas permeability of proposed modified models with existing models in different MMMs shows a better prediction of gas permeability in MMMs.

Keywords: Mixed Matrix Membrane, Permeation Models, Porous particles, Porosity.

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3252 High Capacity Spread-Spectrum Watermarking for Telemedicine Applications

Authors: Basant Kumar, Animesh Anand, S.P. Singh, Anand Mohan

Abstract:

This paper presents a new spread-spectrum watermarking algorithm for digital images in discrete wavelet transform (DWT) domain. The algorithm is applied for embedding watermarks like patient identification /source identification or doctors signature in binary image format into host digital radiological image for potential telemedicine applications. Performance of the algorithm is analysed by varying the gain factor, subband decomposition levels, and size of watermark. Simulation results show that the proposed method achieves higher watermarking capacity.

Keywords: Watermarking, spread-spectrum, discrete wavelettransform, telemedicine

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3251 Enhancement of Tribological Behavior for Diesel Engine Piston of Solid Skirt by an Optimal Choice of Interface Material

Authors: M. Amara, M. Tahar Abbes, A. Dokkiche, M. Benbrike

Abstract:

Shear stresses generate frictional forces thus lead to the reduction of engine performance due to the power losses. This friction can also cause damage to the piston material. Thus, the choice of an optimal material for the piston is necessary to improve the elastohydrodynamical contacts of the piston. In this study, to achieve this objective, an elastohydrodynamical lubrication model that satisfies the best tribological behavior of the piston with the optimum choice of material is developed. Several aluminum alloys composed of different components are studied in this simulation. An application is made on the piston 60 x 120 mm Diesel engine type F8L413 currently mounted on Deutz trucks TB230 by using different aluminum alloys where alloys based on aluminum-silicon have better tribological performance.

Keywords: EHD lubricated contacts, friction, properties of materials, tribological performance.

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3250 An Advanced Method for Speech Recognition

Authors: Meysam Mohamad pour, Fardad Farokhi

Abstract:

In this paper in consideration of each available techniques deficiencies for speech recognition, an advanced method is presented that-s able to classify speech signals with the high accuracy (98%) at the minimum time. In the presented method, first, the recorded signal is preprocessed that this section includes denoising with Mels Frequency Cepstral Analysis and feature extraction using discrete wavelet transform (DWT) coefficients; Then these features are fed to Multilayer Perceptron (MLP) network for classification. Finally, after training of neural network effective features are selected with UTA algorithm.

Keywords: Multilayer perceptron (MLP) neural network, Discrete Wavelet Transform (DWT) , Mels Scale Frequency Filter , UTA algorithm.

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3249 Evaluation of Algorithms for Sequential Decision in Biosonar Target Classification

Authors: Turgay Temel, John Hallam

Abstract:

A sequential decision problem, based on the task ofidentifying the species of trees given acoustic echo data collectedfrom them, is considered with well-known stochastic classifiers,including single and mixture Gaussian models. Echoes are processedwith a preprocessing stage based on a model of mammalian cochlearfiltering, using a new discrete low-pass filter characteristic. Stoppingtime performance of the sequential decision process is evaluated andcompared. It is observed that the new low pass filter processingresults in faster sequential decisions.

Keywords: Classification, neuro-spike coding, parametricmodel, Gaussian mixture with EM algorithm, sequential decision.

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3248 Impulse Response Shortening for Discrete Multitone Transceivers using Convex Optimization Approach

Authors: Ejaz Khan, Conor Heneghan

Abstract:

In this paper we propose a new criterion for solving the problem of channel shortening in multi-carrier systems. In a discrete multitone receiver, a time-domain equalizer (TEQ) reduces intersymbol interference (ISI) by shortening the effective duration of the channel impulse response. Minimum mean square error (MMSE) method for TEQ does not give satisfactory results. In [1] a new criterion for partially equalizing severe ISI channels to reduce the cyclic prefix overhead of the discrete multitone transceiver (DMT), assuming a fixed transmission bandwidth, is introduced. Due to specific constrained (unit morm constraint on the target impulse response (TIR)) in their method, the freedom to choose optimum vector (TIR) is reduced. Better results can be obtained by avoiding the unit norm constraint on the target impulse response (TIR). In this paper we change the cost function proposed in [1] to the cost function of determining the maximum of a determinant subject to linear matrix inequality (LMI) and quadratic constraint and solve the resulting optimization problem. Usefulness of the proposed method is shown with the help of simulations.

Keywords: Equalizer, target impulse response, convex optimization, matrix inequality.

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3247 MMU Simulation in Hardware Simulator Based-on State Transition Models

Authors: Zhang Xiuping, Yang Guowu, Zheng Desheng

Abstract:

Embedded hardware simulator is a valuable computeraided tool for embedded application development. This paper focuses on the ARM926EJ-S MMU, builds state transition models and formally verifies critical properties for the models. The state transition models include loading instruction model, reading data model, and writing data model. The properties of the models are described by CTL specification language, and they are verified in VIS. The results obtained in VIS demonstrate that the critical properties of MMU are satisfied in the state transition models. The correct models can be used to implement the MMU component in our simulator. In the end of this paper, the experimental results show that the MMU can successfully accomplish memory access requests from CPU.

Keywords: MMU, State transition, Model, Simulation.

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3246 Classification of Fuzzy Petri Nets, and Their Applications

Authors: M.H.Aziz, Erik L.J.Bohez, Manukid Parnichkun, Chanchal Saha

Abstract:

Petri Net (PN) has proven to be effective graphical, mathematical, simulation, and control tool for Discrete Event Systems (DES). But, with the growth in the complexity of modern industrial, and communication systems, PN found themselves inadequate to address the problems of uncertainty, and imprecision in data. This gave rise to amalgamation of Fuzzy logic with Petri nets and a new tool emerged with the name of Fuzzy Petri Nets (FPN). Although there had been a lot of research done on FPN and a number of their applications have been anticipated, but their basic types and structure are still ambiguous. Therefore, in this research, an effort is made to categorize FPN according to their structure and algorithms Further, literature review of the applications of FPN in the light of their classifications has been done.

Keywords: Discrete event systems, Fuzzy logic, Fuzzy Petri nets, and Petri nets.

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3245 A Discrete Element Method Centrifuge Model of Monopile under Cyclic Lateral Loads

Authors: Nuo Duan, Yi Pik Cheng

Abstract:

This paper presents the data of a series of two-dimensional Discrete Element Method (DEM) simulations of a large-diameter rigid monopile subjected to cyclic loading under a high gravitational force. At present, monopile foundations are widely used to support the tall and heavy wind turbines, which are also subjected to significant from wind and wave actions. A safe design must address issues such as rotations and changes in soil stiffness subject to these loadings conditions. Design guidance on the issue is limited, so are the availability of laboratory and field test data. The interpretation of these results in sand, such as the relation between loading and displacement, relies mainly on empirical correlations to pile properties. Regarding numerical models, most data from Finite Element Method (FEM) can be found. They are not comprehensive, and most of the FEM results are sensitive to input parameters. The micro scale behaviour could change the mechanism of the soil-structure interaction. A DEM model was used in this paper to study the cyclic lateral loads behaviour. A non-dimensional framework is presented and applied to interpret the simulation results. The DEM data compares well with various set of published experimental centrifuge model test data in terms of lateral deflection. The accumulated permanent pile lateral displacements induced by the cyclic lateral loads were found to be dependent on the characteristics of the applied cyclic load, such as the extent of the loading magnitudes and directions.

Keywords: Cyclic loading, DEM, numerical modelling, sands.

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3244 Sensor Fusion Based Discrete Kalman Filter for Outdoor Robot Navigation

Authors: Mbaitiga Zacharie

Abstract:

The objective of the presented work is to implement the Kalman Filter into an application that reduces the influence of the environmental changes over the robot expected to navigate over a terrain of varying friction properties. The Discrete Kalman Filter is used to estimate the robot position, project the estimated current state ahead at time through time update and adjust the projected estimated state by an actual measurement at that time via the measurement update using the data coming from the infrared sensors, ultrasonic sensors and the visual sensor respectively. The navigation test has been performed in a real world environment and has been found to be robust.

Keywords: Kalman filter, sensors fusion, robot navigation.

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3243 A New Stability Analysis and Stabilization of Discrete-Time Switched Linear Systems Using Vector Norms Approach

Authors: Marwen Kermani, Anis Sakly, Faouzi M'sahli

Abstract:

In this paper, we aim to investigate a new stability analysis for discrete-time switched linear systems based on the comparison, the overvaluing principle, the application of Borne-Gentina criterion and the Kotelyanski conditions. This stability conditions issued from vector norms correspond to a vector Lyapunov function. In fact, the switched system to be controlled will be represented in the Companion form. A comparison system relative to a regular vector norm is used in order to get the simple arrow form of the state matrix that yields to a suitable use of Borne-Gentina criterion for the establishment of sufficient conditions for global asymptotic stability. This proposed approach could be a constructive solution to the state and static output feedback stabilization problems.

Keywords: Discrete-time switched linear systems, Global asymptotic stability, Vector norms, Borne-Gentina criterion, Arrow form state matrix, Arbitrary switching, State feedback controller, Static output feedback controller.

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3242 Neuro-Hybrid Models for Automotive System Identification

Authors: Ventura Assuncao

Abstract:

In automotive systems almost all steps concerning the calibration of several control systems, e.g., low idle governor or boost pressure governor, are made with the vehicle because the timeto- production and cost requirements on the projects do not allow for the vehicle analysis necessary to build reliable models. Here is presented a procedure using parametric and NN (neural network) models that enables the generation of vehicle system models based on normal ECU engine control unit) vehicle measurements. These models are locally valid and permit pre and follow-up calibrations so that, only the final calibrations have to be done with the vehicle.

Keywords: Automotive systems, neuro-hybrid models, demodulator, nonlinear systems, identification, and neural networks.

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3241 A Method to Saturation Modeling of Synchronous Machines in d-q Axes

Authors: Mohamed A. Khlifi, Badr M. Alshammari

Abstract:

This paper discusses the general methods to saturation in the steady-state, two axis (d & q) frame models of synchronous machines. In particular, the important role of the magnetic coupling between the d-q axes (cross-magnetizing phenomenon), is demonstrated. For that purpose, distinct methods of saturation modeling of dumper synchronous machine with cross-saturation are identified, and detailed models synthesis in d-q axes. A number of models are given in the final developed form. The procedure and the novel models are verified by a critical application to prove the validity of the method and the equivalence between all developed models is reported. Advantages of some of the models over the existing ones and their applicability are discussed.

Keywords: Cross-magnetizing, models synthesis, synchronous machine, saturated modeling, state-space vectors.

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3240 Discrete Modified Internal Model Control for a nth-order Plant with an Integrator and Dead-time

Authors: Manato Ono, Hiromitsu Ogawa, Naohiro Ban, Yoshihisa Ishida

Abstract:

This paper deals with a design method of a discrete modified Internal Model Control (IMC) for a plant with an integrator and dead time. If there is a load disturbance in the input or output side of the plant, the proposed control system can eliminate the steady-state error caused by it. The disturbance compensator in this method is simple and its order is low regardless of that of a plant. The simulation studies show that the proposed method has superior performance for a load disturbance rejection and robustness.

Keywords: Internal Model Control, Smith Predictor, Dead time, Integrator.

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3239 GPS and Discrete Kalman Filter for Indoor Robot Navigation

Authors: Mbaitiga Zacharie

Abstract:

This paper discusses the implementation of the Kalman Filter along with the Global Positioning System (GPS) for indoor robot navigation. Two dimensional coordinates is used for the map building, and refers to the global coordinate which is attached to the reference landmark for position and direction information the robot gets. The Discrete Kalman Filter is used to estimate the robot position, project the estimated current state ahead in time through time update and adjust the projected estimated state by an actual measurement at that time via the measurement update. The navigation test has been performed and has been found to be robust.

Keywords: Global positioning System, kalman filter, robot navigation.

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3238 Characteristic of Discrete Raman Amplifier at Different Pump Configurations

Authors: Parekhan M. Jaff

Abstract:

This paper describes the gain and noise performances of discrete Raman amplifier as a function of fiber lengths and the signal input powers for different pump configurations. Simulation has been done by using optisystem 7.0 software simulation at signal wavelength of 1550 nm and a pump wavelength of 1450nm. The results showed that the gain is higher in bidirectional pumping than in counter pumping, the gain changes with increasing the fiber length while the noise figure remain the same for short fiber lengths and the gain saturates differently for different pumping configuration at different fiber lengths and power levels of the signal.

Keywords: Optical Amplifier, Raman Amplifier DiscreteRaman Amplifier (DRA), Wavelength Division Multiplexing(WDM).

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3237 Design of Liquids Mixing Control System using Fuzzy Time Control Discrete Event Model for Industrial Applications

Authors: M.Saleem Khan, Khaled Benkrid

Abstract:

This paper presents a time control liquids mixing system in the tanks as an application of fuzzy time control discrete model. The system is designed for a wide range of industrial applications. The simulation design of control system has three inputs: volume, viscosity, and selection of product, along with the three external control adjustments for the system calibration or to take over the control of the system autonomously in local or distributed environment. There are four controlling elements: rotatory motor, grinding motor, heating and cooling units, and valves selection, each with time frame limit. The system consists of three controlled variables measurement through its sensing mechanism for feed back control. This design also facilitates the liquids mixing system to grind certain materials in tanks and mix with fluids under required temperature controlled environment to achieve certain viscous level. Design of: fuzzifier, inference engine, rule base, deffuzifiers, and discrete event control system, is discussed. Time control fuzzy rules are formulated, applied and tested using MATLAB simulation for the system.

Keywords: Fuzzy time control, industrial application and timecontrol systems, adjustment of Fuzzy system, liquids mixing system, design of fuzzy time control DEV system.

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3236 Classroom Incivility Behaviours among Medical Students: A Comparative Study in Pakistan

Authors: Manal Rauf

Abstract:

Trained medical practitioners are produced from medical colleges serving in public and private sectors. Prime responsibility of teaching faculty is to inculcate required work ethic among the students by serving as role models for them. It is an observed fact that classroom incivility behaviours are providing a friction in achieving these targets. Present study aimed at identification of classroom incivility behaviours observed by teachers and students of public and private medical colleges as per Glasser’s Choice Theory, making a comparison and investigating the strategies being adopted by teachers of both sectors to control undesired class room behaviours. Findings revealed that a significant difference occurs between teacher and student incivility behaviours. Public sector teacher focussed on survival as a strong factor behind in civil behaviours whereas private sector teachers considered power as the precedent for incivility. Teachers of both sectors are required to use verbal as well as non-verbal immediacy to reach a healthy leaning environment.

Keywords: Classroom incivility behaviour, Glasser choice theory, Mehrabian immediacy theory, medical student.

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3235 Stability of a Special Class of Switched Positive Systems

Authors: Xiuyong Ding, Lan Shu, Xiu Liu

Abstract:

This paper is concerned with the existence of a linear copositive Lyapunov function(LCLF) for a special class of switched positive linear systems(SPLSs) composed of continuousand discrete-time subsystems. Firstly, by using system matrices, we construct a special kind of matrices in appropriate manner. Secondly, our results reveal that the Hurwitz stability of these matrices is equivalent to the existence of a common LCLF for arbitrary finite sets composed of continuous- and discrete-time positive linear timeinvariant( LTI) systems. Finally, a simple example is provided to illustrate the implication of our results.

Keywords: Linear co-positive Lyapunov functions, positive systems, switched systems.

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3234 Application of the Discrete-Event Simulation When Optimizing of Business Processes in Trading Companies

Authors: Maxat Bokambayev, Bella Tussupova, Aisha Mamyrova, Erlan Izbasarov

Abstract:

Optimization of business processes in trading companies is reviewed in the report. There is the presentation of the “Wholesale Customer Order Handling Process” business process model applicable for small and medium businesses. It is proposed to apply the algorithm for automation of the customer order processing which will significantly reduce labor costs and time expenditures and increase the profitability of companies. An optimized business process is an element of the information system of accounting of spare parts trading network activity. The considered algorithm may find application in the trading industry as well.

Keywords: Business processes, discrete-event simulation.

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3233 Seismic Behavior of Suction Caisson Foundations

Authors: Mohsen Saleh Asheghabadi, Alireza Jafari Jebeli

Abstract:

Increasing population growth requires more sustainable development of energy. This non-contaminated energy has an inexhaustible energy source. One of the vital parameters in such structures is the choice of foundation type. Suction caissons are now used extensively worldwide for offshore wind turbine. Considering the presence of a number of offshore wind farms in earthquake areas, the study of the seismic behavior of suction caisson is necessary for better design. In this paper, the results obtained from three suction caisson models with different diameter (D) and skirt length (L) in saturated sand were compared with centrifuge test results. All models are analyzed using 3D finite element (FE) method taking account of elasto-plastic Mohr–Coulomb constitutive model for soil which is available in the ABAQUS library. The earthquake load applied to the base of models with a maximum acceleration of 0.65g. The results showed that numerical method is in relative good agreement with centrifuge results. The settlement and rotation of foundation decrease by increasing the skirt length and foundation diameter. The sand soil outside the caisson is prone to liquefaction due to its low confinement.

Keywords: Liquefaction, suction caisson foundation, offshore wind turbine, numerical analysis, seismic behavior.

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3232 Losses Analysis in TEP Considering Uncertainity in Demand by DPSO

Authors: S. Jalilzadeh, A. Kimiyaghalam, A. Ashouri

Abstract:

This paper presents a mathematical model and a methodology to analyze the losses in transmission expansion planning (TEP) under uncertainty in demand. The methodology is based on discrete particle swarm optimization (DPSO). DPSO is a useful and powerful stochastic evolutionary algorithm to solve the large-scale, discrete and nonlinear optimization problems like TEP. The effectiveness of the proposed idea is tested on an actual transmission network of the Azerbaijan regional electric company, Iran. The simulation results show that considering the losses even for transmission expansion planning of a network with low load growth is caused that operational costs decreases considerably and the network satisfies the requirement of delivering electric power more reliable to load centers.

Keywords: DPSO, TEP, Uncertainty

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3231 Comparison of S-transform and Wavelet Transform in Power Quality Analysis

Authors: Mohammad Javad Dehghani

Abstract:

In the power quality analysis non-stationary nature of voltage distortions require some precise and powerful analytical techniques. The time-frequency representation (TFR) provides a powerful method for identification of the non-stationary of the signals. This paper investigates a comparative study on two techniques for analysis and visualization of voltage distortions with time-varying amplitudes. The techniques include the Discrete Wavelet Transform (DWT), and the S-Transform. Several power quality problems are analyzed using both the discrete wavelet transform and S–transform, showing clearly the advantage of the S– transform in detecting, localizing, and classifying the power quality problems.

Keywords: Power quality, S-Transform, Short Time FourierTransform , Wavelet Transform, instantaneous sag, swell.

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3230 Extended Set of DCT-TPLBP and DCT-FPLBP for Face Recognition

Authors: El Mahdi Barrah, Said Safi, Abdessamad Malaoui

Abstract:

In this paper, we describe an application for face recognition. Many studies have used local descriptors to characterize a face, the performance of these local descriptors remain low by global descriptors (working on the entire image). The application of local descriptors (cutting image into blocks) must be able to store both the advantages of global and local methods in the Discrete Cosine Transform (DCT) domain. This system uses neural network techniques. The letter method provides a good compromise between the two approaches in terms of simplifying of calculation and classifying performance. Finally, we compare our results with those obtained from other local and global conventional approaches.

Keywords: Face detection, face recognition, discrete cosine transform (DCT), FPLBP, TPLBP, NN.

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3229 Dynamic Models versus Frailty Models for Recurrent Event Data

Authors: Entisar A. Elgmati

Abstract:

Recurrent event data is a special type of multivariate survival data. Dynamic and frailty models are one of the approaches that dealt with this kind of data. A comparison between these two models is studied using the empirical standard deviation of the standardized martingale residual processes as a way of assessing the fit of the two models based on the Aalen additive regression model. Here we found both approaches took heterogeneity into account and produce residual standard deviations close to each other both in the simulation study and in the real data set.

Keywords: Dynamic, frailty, misspecification, recurrent events.

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3228 Sharing Tourism Experience through Social Media: Consumer's Behavioral Intention for Destination Choice

Authors: Mohammad Tipu Sultan, Farzana Sharmin, Ke Xue

Abstract:

Social media create a better opportunity for travelers to search for travel information, select destination and share their personal experiences of the travel. This study proposes a framework which describes the relationships between social media, and positive or negative tourism experience sharing impact on destination choice. To find out new trends of travelers behavioral intention, we propose an extended theoretical model, the Theory of Reasoned Action (TRA). We conducted a survey to analyze three external factors, subjective norms, and positive and negative experience influence on travel destination choice. Structural questionnaire analysis was employed to confirm the proposed research hypothesis within the relationship between consumer influences on the shared experience of social media. The results of the study confirm that sharing positive experiences influence the positive effect of destination choice, while negative experiences decrease the destination selection option. The results indicate that attitudes, subjective norms are passively influenced by shared experience. Moreover, we find that sharing live pictures of travel experiences through social media helps to reduce negative perceptions of the destination brand. This research contribution is useable to the research field as a new determination factor and the findings could be used by destination organization management (DMO) to enhancing their tourism promotion through social media.

Keywords: Destination choice, tourism experience sharing, Theory of Reasoned Action, social media.

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3227 Development of an Efficient CVT using Electromecanical System

Authors: A. A. Shafie, M. H. Ali

Abstract:

Continuously variable transmission (CVT) is a type of automatic transmission that can change the gear ratio to any arbitrary setting within the limits. The most common type of CVT operates on a pulley system that allows an infinite variability between highest and lowest gears with no discrete steps. However, the current CVT system with hydraulic actuation method suffers from the power loss. It needs continuous force for the pulley to clamp the belt and hold the torque resulting in large amount of energy consumption. This study focused on the development of an electromechanical actuated control CVT to eliminate the problem that faced by the existing CVT. It is conducted with several steps; computing and selecting the appropriate sizing for stroke length, lead screw system and etc. From the visual observation it was found that the CVT system of this research is satisfactory.

Keywords: CVT, Hydraulic Actuator, Discrete shifts, Electromechanical system, Lead screws.

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3226 An Engineering Approach to Forecast Volatility of Financial Indices

Authors: Irwin Ma, Tony Wong, Thiagas Sankar

Abstract:

By systematically applying different engineering methods, difficult financial problems become approachable. Using a combination of theory and techniques such as wavelet transform, time series data mining, Markov chain based discrete stochastic optimization, and evolutionary algorithms, this work formulated a strategy to characterize and forecast non-linear time series. It attempted to extract typical features from the volatility data sets of S&P100 and S&P500 indices that include abrupt drops, jumps and other non-linearity. As a result, accuracy of forecasting has reached an average of over 75% surpassing any other publicly available results on the forecast of any financial index.

Keywords: Discrete stochastic optimization, genetic algorithms, genetic programming, volatility forecast

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3225 A Microscopic Simulation Model for Earthmoving Operations

Authors: Jiali Fu

Abstract:

Earthmoving operations are a major part of many construction projects. Because of the complexity and fast-changing environment of such operations, the planning and estimating are crucial on both planning and operational levels. This paper presents the framework ofa microscopic discrete-event simulation system for modeling earthmoving operations and conducting productivity estimations on an operational level.A prototype has been developed to demonstrate the applicability of the proposed framework, and this simulation system is presented via a case study based on an actual earthmoving project. The case study shows that the proposed simulation model is capable of evaluating alternative operating strategies and resource utilization at a very detailed level.

Keywords: Earthmoving operation, microscopic simulation, discrete-event simulation

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3224 Numerical Treatment of Block Method for the Solution of Ordinary Differential Equations

Authors: A. M. Sagir

Abstract:

Discrete linear multistep block method of uniform order for the solution of first order initial value problems (IVP­s­) in ordinary differential equations (ODE­s­) is presented in this paper. The approach of interpolation and collocation approximation are adopted in the derivation of the method which is then applied to first order ordinary differential equations with associated initial conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain four discrete schemes, which were used in block form for parallel or sequential solutions of the problems. Furthermore, a stability analysis and efficiency of the block method are tested on ordinary differential equations, and the results obtained compared favorably with the exact solution.

Keywords: Block Method, First Order Ordinary Differential Equations, Hybrid, Self starting.

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