Search results for: second and third order derivatives

Authors: M. Sedighizadeh, A. Rezazadeh

Abstract:

In this paper presents a technique for developing the computational efficiency in simulating double output induction generators (DOIG) with two rotor circuits where stator transients are to be included. Iterative decomposition is used to separate the flux– Linkage equations into decoupled fast and slow subsystems, after which the model order of the fast subsystems is reduced by neglecting the heavily damped fast transients caused by the second rotor circuit using integral manifolds theory. The two decoupled subsystems along with the equation for the very slowly changing slip constitute a three time-scale model for the machine which resulted in increasing computational speed. Finally, the proposed method of reduced order in this paper is compared with the other conventional methods in linear and nonlinear modes and it is shown that this method is better than the other methods regarding simulation accuracy and speed.

Keywords: DOIG, Iterative separation, Integral manifolds, Reduced order.

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Authors: Mohammed Zidane, Said Safi, Mohamed Sabri, Ahmed Boumezzough

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In this paper we propose an algorithm based on higher order cumulants, for blind impulse response identification of frequency radio channels and downlink (MC−CDMA) system Equalization. In order to test its efficiency, we have compared with another algorithm proposed in the literature, for that we considered on theoretical channel as the Proakis’s ‘B’ channel and practical frequency selective fading channel, called Broadband Radio Access Network (BRAN C), normalized for (MC−CDMA) systems, excited by non-Gaussian sequences. In the part of (MC−CDMA), we use the Minimum Mean Square Error (MMSE) equalizer after the channel identification to correct the channel’s distortion. The simulation results, in noisy environment and for different signal to noise ratio (SNR), are presented to illustrate the accuracy of the proposed algorithm.

Keywords: Blind identification and equalization, Higher Order Cumulants, (MC−CDMA) system, MMSE equalizer.

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Authors: Swadhin Ku. Mishra, Sidhartha Panda, Simanchala Padhy, C. Ardil

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In this paper, real-coded genetic algorithm (RCGA) optimization technique has been applied for large-scale linear dynamic multi-input-multi-output (MIMO) system. The method is based on error minimization technique where the integral square error between the transient responses of original and reduced order models has been minimized by RCGA. The reduction procedure is simple computer oriented and the approach is comparable in quality with the other well-known reduction techniques. Also, the proposed method guarantees stability of the reduced model if the original high-order MIMO system is stable. The proposed approach of MIMO system order reduction is illustrated with the help of an example and the results are compared with the recently published other well-known reduction techniques to show its superiority.

Keywords: Multi-input-multi-output (MIMO) system.Modelorder reduction. Integral squared error (ISE). Real-coded geneticalgorithm

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Authors: Tarek Fatouh, Chehab Elbelehy, Alaa Abdelsalam, Eman Elakkad, Alaa Abdelshafie

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This paper aims to explore the possibility of time compression in Engineer to Order production networks. A case study research method is used in a Norwegian shipbuilding project by implementing a value stream mapping lean tool with total cycle time as a unit of analysis. The analysis resulted in demonstrating the time deviations for the planned tasks in one of the processes in the shipbuilding project. So, authors developed a future state map by removing time wastes from value stream process.

Keywords: Engineer to order, total cycle time, value stream mapping, shipbuilding.

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Authors: Yashar Haghighatfar, Shahrzad Mirhosseini

Abstract:

Pull-in instability is a nonlinear and crucial effect that is important for the design of microelectromechanical system devices. In this paper, the appropriate electrostatic voltage range is determined by measuring fluid flow pressure via micro pressure sensor based microbeam. The microbeam deflection contains two parts, the static and perturbation deflection of static. The second order equation regarding the equivalent stiffness, mass and damping matrices based on Galerkin method is introduced to predict pull-in instability due to the external voltage. Also the reduced order method is used for solving the second order nonlinear equation of motion. Furthermore, in the present study, the micro capacitive pressure sensor is designed for measuring special fluid flow pressure range. The results show that the measurable pressure range can be optimized, regarding damping field and external voltage.

Keywords: MEMS, pull-in instability, electrostatically actuated microbeam, reduced order method.

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Authors: Theologos Athanaselis, Stelios Bakamidis, Ioannis Dologlou, Konstantinos Mamouras

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This paper presents an approach for repairing word order errors in English text by reordering words in a sentence and choosing the version that maximizes the number of trigram hits according to a language model. A possible way for reordering the words is to use all the permutations. The problem is that for a sentence with length N words the number of all permutations is N!. The novelty of this method concerns the use of an efficient confusion matrix technique for reordering the words. The confusion matrix technique has been designed in order to reduce the search space among permuted sentences. The limitation of search space is succeeded using the statistical inference of N-grams. The results of this technique are very interesting and prove that the number of permuted sentences can be reduced by 98,16%. For experimental purposes a test set of TOEFL sentences was used and the results show that more than 95% can be repaired using the proposed method.

Keywords: Permutations filtering, Statistical language model N-grams, Word order errors, TOEFL

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Authors: Norhashidah Hj. Mohd Ali, Teng Wai Ping

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In this paper, the formulation of a new group explicit method with a fourth order accuracy is described in solving the two dimensional Helmholtz equation. The formulation is based on the nine-point fourth order compact finite difference approximation formula. The complexity analysis of the developed scheme is also presented. Several numerical experiments were conducted to test the feasibility of the developed scheme. Comparisons with other existing schemes will be reported and discussed. Preliminary results indicate that this method is a viable alternative high accuracy solver to the Helmholtz equation.

Keywords: Explicit group method, finite difference, Helmholtz equation, five-point formula, nine-point formula.

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Authors: K. K. Yong, R. Mahmud, C. S. Woo

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Data mining and knowledge engineering have become a tough task due to the availability of large amount of data in the web nowadays. Validity and reliability of data also become a main debate in knowledge acquisition. Besides, acquiring knowledge from different languages has become another concern. There are many language translators and corpora developed but the function of these translators and corpora are usually limited to certain languages and domains. Furthermore, search results from engines with traditional 'keyword' approach are no longer satisfying. More intelligent knowledge engineering agents are needed. To address to these problems, a system known as Multilingual Word Semantic Network is proposed. This system adapted semantic network to organize words according to concepts and relations. The system also uses open source as the development philosophy to enable the native language speakers and experts to contribute their knowledge to the system. The contributed words are then defined and linked using lexical and semantic relations. Thus, related words and derivatives can be identified and linked. From the outcome of the system implementation, it contributes to the development of semantic web and knowledge engineering.

Keywords: Multilingual, semantic network, intelligent knowledge engineering.

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Authors: Shiann-Shiun Jeng, Jia-Ming Chen, Hong-Zong Lin, Chen-Wan Tsung

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For cognitive radio networks, there is a major spectrum sensing problem, i.e. dynamic spectrum management. It is an important issue to sense and identify the spectrum holes in cognitive radio networks. The first-order derivative scheme is usually used to detect the edge of the spectrum. In this paper, a novel spectrum sensing technique for cognitive radio is presented. The proposed algorithm offers efficient edge detection. Then, simulation results show the performance of the first-order derivative scheme and the proposed scheme and depict that the proposed scheme obtains better performance than does the first-order derivative scheme.

Keywords: cognitive radio, Spectrum Sensing, wavelet, edgedetection

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Authors: Samson Okwakol Ariko, Venansius Baryamureeba

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Internet Access Technologies (IAT) provide a means through which Internet can be accessed. The choice of a suitable Internet technology is increasingly becoming an important issue to ISP clients. Currently, the choice of IAT is based on discretion and intuition of the concerned managers and the reliance on ISPs. In this paper we propose a model and designs algorithms that are used in the Internet access technology specification. In the proposed model, three ranking approaches are introduced; concurrent ranking, stepwise ranking and weighted ranking. The model ranks the IAT based on distance measures computed in ascending order while the global ranking system assigns weights to each IAT according to the position held in each ranking technique, determines the total weight of a particular IAT and ranks them in descending order. The final output is an objective ranking of IAT in descending order.

Keywords: Internet Access Technology (IAT).

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Authors: Chungkuk Jin, Moohyun Kim, Woo Chul Chung

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This paper presents global performance and dynamic behaviors of a discrete-pontoon-type floating bridge with mooring lines in time domain under wind and wave excitations. The structure is designed for long-distance and deep-water crossing and consists of the girder, columns, pontoons, and mooring lines. Their functionality and behaviors are investigated by using elastic-floater/mooring fully-coupled dynamic simulation computer program. Dynamic wind, first- and second-order wave forces, and current loads are considered as environmental loads. Girder’s dynamic responses and mooring tensions are analyzed under different analysis methods and environmental conditions. Girder’s lateral responses are highly influenced by the second-order wave and wind loads while the first-order wave load mainly influences its vertical responses.

Keywords: Floating bridge, elastic dynamic response, coupled dynamics, mooring line, pontoon, wave/wind excitation, resonance, second-order effect.

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Authors: M. Karami Khorramabadi, A. R. Nezamabadi

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Stability of functionally graded beams with piezoelectric layers subjected to axial compressive load that is simply supported at both ends is studied in this paper. The displacement field of beam is assumed based on first order shear deformation beam theory. Applying the Hamilton's principle, the governing equation is established. The influences of applied voltage, dimensionless geometrical parameter, functionally graded index and piezoelectric thickness on the critical buckling load of beam are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data.

Keywords: Stability, Functionally graded beam, First order shear deformation theory, Piezoelectric layer.

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Authors: S. Mat Radzi, N. J. Abd Rahman, H. Mohd Noor, N. Ariffin

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Ferulic acid has widespread industrial potential by virtue of its antioxidant properties. However, it is partially soluble in aqueous media, limiting their usefulness in oil-based processes in food, cosmetic, pharmaceutical, and material industry. Therefore, modification of ferulic acid should be made by producing of more lipophilic derivatives. In this study, a preliminary investigation of lipase-catalyzed trans-esterification reaction of ethyl ferulate and olive oil was investigated. The reaction was catalyzed by immobilized lipase from Candida antarctica (Novozym 435), to produce ferulate ester, a sunscreen agent. A statistical approach of Response surface methodology (RSM) was used to evaluate the interactive effects of reaction temperature (40-80°C), reaction time (4-12 hours), and amount of enzyme (0.1-0.5 g). The optimum conditions derived via RSM were reaction temperature 60°C, reaction time 2.34 hours, and amount of enzyme 0.3 g. The actual experimental yield was 59.6% ferulate ester under optimum condition, which compared well to the maximum predicted value of 58.0%.

Keywords: Ferulic acid, Enzymatic Synthesis, Esters, RSM.

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Authors: Olusheye Akinfenwa, Samuel Jator, Nianmin Yoa

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A block backward differentiation formula of uniform order eight is proposed for solving first order stiff initial value problems (IVPs). The conventional 8-step Backward Differentiation Formula (BDF) and additional methods are obtained from the same continuous scheme and assembled into a block matrix equation which is applied to provide the solutions of IVPs on non-overlapping intervals. The stability analysis of the method indicates that the method is L0-stable. Numerical results obtained using the proposed new block form show that it is attractive for solutions of stiff problems and compares favourably with existing ones.

Keywords: Stiff IVPs, System of ODEs, Backward differentiationformulas, Block methods, Stability.

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Authors: Pravin S. Bodke, Shradha S. Binani, Ravi V. Joat

Abstract:

Science and technology of ultrasonic is widely used in recent years for industrial and medicinal application. The acoustical properties of 2-mercapto substituted pyrimidines viz.,2- Mercapto-4- (2’,4’ –dichloro phenyl) – 6-(2’ – hydroxyl -4’ –methyl-5’ – chlorophenyl) pyrimidine and 2 –Mercapto – 4-(4’ –chloro phenyl) – 6-(2’ – hydroxyl -4’ –methyl-5’ –chlorophenyl) pyrimidine have been investigated from the ultrasonic velocity and density measurements at different concentration and different % in dioxane-water mixture at 305K. The adiabatic compressibility (βs), acoustic impedance (Z), intermolecular free length (Lf), apparent molar volume(ϕv) and relative association (RA) values have been calculated from the experimental data of velocity and density measurement at concentration range of 0.01- 0.000625 mol/lit and 70%,75% and 80% dioxane water mixture. These above parameters are used to discuss the structural and molecular interactions.

Keywords: Acoustical parameters, Density, Dioxane-water mixture, Ultrasonic velocity.

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Authors: Birs Isabela, Muresan Cristina, Folea Silviu, Prodan Ovidiu

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The wing is one of the most important parts of an airplane because it ensures stability, sustenance and maneuverability of the airplane. Because of its shape, the airplane wing can be simplified to a smart beam. Active vibration suppression is realized using piezoelectric actuators that are mounted on the surface of the beam. This work presents a tuning procedure of fractional order controllers based on a graphical approach of the frequency domain representation. The efficacy of the method is proven by practically testing the controller on a laboratory scale experimental stand.

Keywords: Fractional order controller, piezoelectric actuators, smart beam, vibration suppression.

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Authors: Yang Liu, Hong Li, Siriguleng He, Wei Gao, Zhichao Fang

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In this paper, the C1-conforming finite element method is analyzed for a class of nonlinear fourth-order hyperbolic partial differential equation. Some a priori bounds are derived using Lyapunov functional, and existence, uniqueness and regularity for the weak solutions are proved. Optimal error estimates are derived for both semidiscrete and fully discrete schemes.

Keywords: Nonlinear fourth-order hyperbolic equation, Lyapunov functional, existence, uniqueness and regularity, conforming finite element method, optimal error estimates.

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Authors: Salah Alrabeei, Mohammad Yousuf

Abstract:

The goal of option pricing theory is to help the investors to manage their money, enhance returns and control their financial future by theoretically valuing their options. However, most of the option pricing models have no analytical solution. Furthermore, not all the numerical methods are efficient to solve these models because they have nonsmoothing payoffs or discontinuous derivatives at the exercise price. In this paper, we solve the American option under jump diffusion models by using efficient time-dependent numerical methods. several techniques are integrated to reduced the overcome the computational complexity. Fast Fourier Transform (FFT) algorithm is used as a matrix-vector multiplication solver, which reduces the complexity from O(M2) into O(M logM). Partial fraction decomposition technique is applied to rational approximation schemes to overcome the complexity of inverting polynomial of matrices. The proposed method is easy to implement on serial or parallel versions. Numerical results are presented to prove the accuracy and efficiency of the proposed method.

Keywords: Integral differential equations, American options, jump–diffusion model, rational approximation.

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Authors: J. S. Yadav, N. P. Patidar, J. Singhai, S. Panda, C. Ardil

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In this paper a mixed method by combining an evolutionary and a conventional technique is proposed for reduction of Single Input Single Output (SISO) continuous systems into Reduced Order Model (ROM). In the conventional technique, the mixed advantages of Mihailov stability criterion and continued Fraction Expansions (CFE) technique is employed where the reduced denominator polynomial is derived using Mihailov stability criterion and the numerator is obtained by matching the quotients of the Cauer second form of Continued fraction expansions. Then, retaining the numerator polynomial, the denominator polynomial is recalculated by an evolutionary technique. In the evolutionary method, the recently proposed Differential Evolution (DE) optimization technique is employed. DE method is based on the minimization of the Integral Squared Error (ISE) between the transient responses of original higher order model and the reduced order model pertaining to a unit step input. The proposed method is illustrated through a numerical example and compared with ROM where both numerator and denominator polynomials are obtained by conventional method to show its superiority.

Keywords: Reduced Order Modeling, Stability, Mihailov Stability Criterion, Continued Fraction Expansions, Differential Evolution, Integral Squared Error.

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Authors: Norhashidah Hj. Mohd Ali, Teng Wai Ping

Abstract:

In this paper, we present a high order group explicit method in solving the two dimensional Helmholtz equation. The presented method is derived from a nine-point fourth order finite difference approximation formula obtained from a 45-degree rotation of the standard grid which makes it possible for the construction of iterative procedure with reduced complexity. The developed method will be compared with the existing group iterative schemes available in literature in terms of computational time, iteration counts, and computational complexity. The comparative performances of the methods will be discussed and reported.

Keywords: Explicit group method, finite difference, Helmholtz equation, rotated grid, standard grid.

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Authors: M. Trinidad Pérez-Palacios, Catarina Petisca, Olívia Pinho, Isabel M.P.L.V.O. Ferreira

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This work evaluated the effect of temperature on headspace solid-phase microextraction of volatile and furanic compounds in coated fish sticks. The major goal was the analysis of the samples as consumed, to reproduce volatile compounds people feel when consuming those products. Extraction at 37 ºC (the human body temperature) throughout the HS-SPME analysis of volatile and furanic compounds in coated fish was compared with higher extraction temperatures, which are frequently used for this kind of determinations. The profile of volatile compounds found in deepfried (F) and non-fried (NF) coated fish at 37 and 50 ºC was different from that obtained at 80 ºC. Concerning furan and its derivatives, an extra formation of these compounds was observed at higher extraction temperatures. The analysis of volatile and furanic compounds in fish coated sticks simulating the cooking and eating conditions can be reliably carried out setting the headspace absorption temperature at 37 ºC.

Keywords: Analysis of samples as consumed, fish coated sticks, furans, headspace extraction temperature, volatiles.

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Authors: M. A. Tayfun

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Occurrences of spurious crests on the troughs of large, relatively steep second-order Stokes waves are anomalous and not an inherent characteristic of real waves. Here, the effects of such occurrences on the statistics described by the standard second-order stochastic model are examined theoretically and by way of simulations. Theoretical results and simulations indicate that when spurious occurrences are sufficiently large, the standard model leads to physically unrealistic surface features and inaccuracies in the statistics of various surface features, in particular, the troughs and thus zero-crossing heights of large waves. Whereas inaccuracies can be fairly noticeable for long-crested waves in both deep and shallower depths, they tend to become relatively insignificant in directional waves.

Keywords: Large waves, non-linear effects, simulation, spectra, spurious crests, Stokes waves, wave breaking, wave statistics.

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Authors: Reza Mohammadi, Mahdieh Sahebi

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We develop a method based on polynomial quintic spline for numerical solution of fourth-order non-homogeneous parabolic partial differential equation with variable coefficient. By using polynomial quintic spline in off-step points in space and finite difference in time directions, we obtained two three level implicit methods. Stability analysis of the presented method has been carried out. We solve four test problems numerically to validate the derived method. Numerical comparison with other methods shows the superiority of presented scheme.

Keywords: Fourth-order parabolic equation, variable coefficient, polynomial quintic spline, off-step points, stability analysis.

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Authors: Faris Elghaish, Sepehr Abrishami, Mark Gaterell, Richard Wise

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The collaboration and integration between all building information management (BIM) processes and tasks are necessary to ensure that all project objectives can be delivered. The literature review has been used to explore the state of the art BIM technologies to manage construction materials as well as the challenges which have faced the construction process using traditional methods. Thus, this paper aims to articulate a framework to integrate traditional material planning methods such as ABC analysis theory (Pareto principle) to analyse and categorise the project materials, as well as using independent material planning methods such as Economic Order Quantity (EOQ) and Fixed Order Point (FOP) into the BIM 4D, and 5D capabilities in order to articulate a dependent material planning cycle into BIM, which relies on the constructability method. Moreover, we build a model to connect between the material planning outputs and the BIM 4D and 5D data to ensure that all project information will be accurately presented throughout integrated and complementary BIM reporting formats. Furthermore, this paper will present a method to integrate between the risk management output and the material management process to ensure that all critical materials are monitored and managed under the all project stages. The paper includes browsers which are proposed to be embedded in any 4D BIM platform in order to predict the EOQ as well as FOP and alarm the user during the construction stage. This enables the planner to check the status of the materials on the site as well as to get alarm when the new order will be requested. Therefore, this will lead to manage all the project information in a single context and avoid missing any information at early design stage. Subsequently, the planner will be capable of building a more reliable 4D schedule by allocating the categorised material with the required EOQ to check the optimum locations for inventory and the temporary construction facilitates.

Keywords: Building information management, BIM, economic order quantity, fixed order point, BIM 4D, BIM 5D.

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Authors: N. Ould Cherchali, A. Tlemçani, M. S. Boucherit, A. Morsli

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Nature-inspired metaheuristic algorithms, particularly those founded on swarm intelligence, have attracted much attention over the past decade. Firefly algorithm has appeared in approximately seven years ago, its literature has enlarged considerably with different applications. It is inspired by the behavior of fireflies. The aim of this paper is the application of firefly algorithm for solving a nonlinear algebraic system. This resolution is needed to study the Selective Harmonic Eliminated Pulse Width Modulation strategy (SHEPWM) to eliminate the low order harmonics; results have been applied on multilevel inverters. The final results from simulations indicate the elimination of the low order harmonics as desired. Finally, experimental results are presented to confirm the simulation results and validate the efficaciousness of the proposed approach.

Keywords: Firefly algorithm, metaheuristic algorithm, multilelvel inverter, SHEPWM.

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Authors: Fuziyah Ishak, Mohamed B. Suleiman, Zanariah A. Majid, Khairil I. Othman

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This paper considers the development of a two-point predictor-corrector block method for solving delay differential equations. The formulae are represented in divided difference form and the algorithm is implemented in variable stepsize variable order technique. The block method produces two new values at a single integration step. Numerical results are compared with existing methods and it is evident that the block method performs very well. Stability regions of the block method are also investigated.

Keywords: block method, delay differential equations, predictor-corrector, stability region, variable stepsize variable order.

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Authors: Ameur Abdelkader, Abed Bouarfa Hafida

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Since its inception, predictive analysis has revolutionized the IT industry through its robustness and decision-making facilities. It involves the application of a set of data processing techniques and algorithms in order to create predictive models. Its principle is based on finding relationships between explanatory variables and the predicted variables. Past occurrences are exploited to predict and to derive the unknown outcome. With the advent of big data, many studies have suggested the use of predictive analytics in order to process and analyze big data. Nevertheless, they have been curbed by the limits of classical methods of predictive analysis in case of a large amount of data. In fact, because of their volumes, their nature (semi or unstructured) and their variety, it is impossible to analyze efficiently big data via classical methods of predictive analysis. The authors attribute this weakness to the fact that predictive analysis algorithms do not allow the parallelization and distribution of calculation. In this paper, we propose to extend the predictive analysis algorithm, Classification And Regression Trees (CART), in order to adapt it for big data analysis. The major changes of this algorithm are presented and then a version of the extended algorithm is defined in order to make it applicable for a huge quantity of data.

Keywords: Predictive analysis, big data, predictive analysis algorithms. CART algorithm.

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Authors: Kashif Bilal, Tassawar Iqbal, Asad Ali Safi, Nadeem Daudpota

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This paper deals with dynamic load balancing using PVM. In distributed environment Load Balancing and Heterogeneity are very critical issues and needed to drill down in order to achieve the optimal results and efficiency. Various techniques are being used in order to distribute the load dynamically among different nodes and to deal with heterogeneity. These techniques are using different approaches where Process Migration is basic concept with different optimal flavors. But Process Migration is not an easy job, it impose lot of burden and processing effort in order to track each process in nodes. We will propose a dynamic load balancing technique in which application will intelligently balance the load among different nodes, resulting in efficient use of system and have no overheads of process migration. It would also provide a simple solution to problem of load balancing in heterogeneous environment.

Keywords: PVM, load balancing, task allocation, intelligent application.

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Authors: K. V. Geetha, N. R. Mangalambal

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Aim. We have introduced the notion of order to multinormed spaces and countable union spaces and their duals. The topology of bounded convergence is assigned to the dual spaces. The aim of this paper is to develop the theory of ordered topological linear spaces La,b, L(w, z), the dual spaces of ordered multinormed spaces La,b, ordered countable union spaces L(w, z), with the topology of bounded convergence assigned to the dual spaces. We apply Laplace transformation to the ordered linear space of Laplace transformable generalized functions. We ultimately aim at finding solutions to nonhomogeneous nth order linear differential equations with constant coefficients in terms of generalized functions and comparing different solutions evolved out of different initial conditions. Method. The above aim is achieved by • Defining the spaces La,b, L(w, z). • Assigning an order relation on these spaces by identifying a positive cone on them and studying the properties of the cone. • Defining an order relation on the dual spaces La,b, L(w, z) of La,b, L(w, z) and assigning a topology to these dual spaces which makes the order dual and the topological dual the same. • Defining the adjoint of a continuous map on these spaces and studying its behaviour when the topology of bounded convergence is assigned to the dual spaces. • Applying the two-sided Laplace Transformation on the ordered linear space of generalized functions W and studying some properties of the transformation which are used in solving differential equations. Result. The above techniques are applied to solve non-homogeneous n-th order linear differential equations with constant coefficients in terms of generalized functions and to compare different solutions of the differential equation.

Keywords: Laplace transformable generalized function, positive cone, topology of bounded convergence

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Authors: Naveed Ahmed, Gunar Matthies

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We deal with the numerical solution of time-dependent convection-diffusion-reaction equations. We combine the local projection stabilization method for the space discretization with two different time discretization schemes: the continuous Galerkin-Petrov (cGP) method and the discontinuous Galerkin (dG) method of polynomial of degree k. We establish the optimal error estimates and present numerical results which shows that the cGP(k) and dG(k)- methods are accurate of order k +1, respectively, in the whole time interval. Moreover, the cGP(k)-method is superconvergent of order 2k and dG(k)-method is of order 2k +1 at the discrete time points. Furthermore, the dependence of the results on the choice of the stabilization parameter are discussed and compared.

Keywords: Convection-diffusion-reaction equations, stabilized finite elements, discontinuous Galerkin, continuous Galerkin-Petrov.

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