Search results for: collocation errors

Authors: Y. Mohseniahouei, K. Abdella, M. Pollanen

Abstract:

In this paper, we explore the applicability of the Sinc- Collocation method to a three-dimensional (3D) oceanography model. The model describes a wind-driven current with depth-dependent eddy viscosity in the complex-velocity system. In general, the Sinc-based methods excel over other traditional numerical methods due to their exponentially decaying errors, rapid convergence and handling problems in the presence of singularities in end-points. Together with these advantages, the Sinc-Collocation approach that we utilize exploits first derivative interpolation, whose integration is much less sensitive to numerical errors. We bring up several model problems to prove the accuracy, stability, and computational efficiency of the method. The approximate solutions determined by the Sinc-Collocation technique are compared to exact solutions and those obtained by the Sinc-Galerkin approach in earlier studies. Our findings indicate that the Sinc-Collocation method outperforms other Sinc-based methods in past studies.

Keywords: Boundary Value Problems, Differential Equations, Sinc Numerical Methods, Wind-Driven Currents

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Authors: Fatima Muhammad Shitu

Abstract:

In language learning, second language learners as well as Native speakers commit errors in their attempt to achieve competence in the target language. The realm of collocation has to do with meaning relation between lexical items. In all human language, there is a kind of ‘natural order’ in which words are arranged or relate to one another in sentences so much so that when a word occurs in a given context, the related or naturally co-occurring word will automatically come to the mind. It becomes an error, therefore, if students inappropriately pair or arrange such ‘naturally’ co–occurring lexical items in a text. It has been observed that most of the second language learners in this research group commit collocation errors. A study of this kind is very significant as it gives insight into the kinds of errors committed by learners. This will help the language teacher to be able to identify the sources and causes of such errors as well as correct them thereby guiding, helping and leading the learners towards achieving some level of competence in the language. The aim of the study is to understand the nature of these errors as stumbling blocks to effective essay writing. The objective of the study is to identify the errors, analyze their structural compositions so as to determine whether there are similarities between students in this regard and to find out whether there are patterns to these kinds of errors which will enable the researcher to understand their sources and causes. As a descriptive research, the researcher samples some nine hundred essays collected from three hundred undergraduate learners of English as a second language in the Federal College of Education, Kano, North- West Nigeria, i.e. three essays per each student. The essays which were given on three different lecture times were of similar thematic preoccupations (i.e. same topics) and length (i.e. same number of words). The essays were written during the lecture hour at three different lecture occasions. The errors were identified in a systematic manner whereby errors so identified were recorded only once even if they occur severally in students’ essays. The data was collated using percentages in which the identified numbers of occurrences were converted accordingly in percentages. The findings from the study indicate that there are similarities as well as regular and repeated errors which provided a pattern. Based on the pattern identified, the conclusion is that students’ collocation errors are attributable to poor teaching and learning which resulted in wrong generalization of rules.

Keywords: Collocations, errors, collocation errors, second language learning.

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Authors: Junghan Kim, Wonkyu Chung, Sunyoung Bu, Philsu Kim

Abstract:

In this paper, we introduce a generalized Chebyshev collocation method (GCCM) based on the generalized Chebyshev polynomials for solving stiff systems. For employing a technique of the embedded Runge-Kutta method used in explicit schemes, the property of the generalized Chebyshev polynomials is used, in which the nodes for the higher degree polynomial are overlapped with those for the lower degree polynomial. The constructed algorithm controls both the error and the time step size simultaneously and further the errors at each integration step are embedded in the algorithm itself, which provides the efficiency of the computational cost. For the assessment of the effectiveness, numerical results obtained by the proposed method and the Radau IIA are presented and compared.

Keywords: Generalized Chebyshev Collocation method, Generalized Chebyshev Polynomial, Initial value problem.

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Authors: A. E. Emam, M. Abd Elghany

Abstract:

The change in orbit evolution between collocated satellites (X, Y) inside +/-0.09° E/W and +/- 0.07° N/S cluster, after one of these satellites is placed in an inclined orbit (satellite X) and the effect of this change in the collocation safety inside the cluster window has been studied and evaluated. Several collocation scenarios had been studied in order to adjust the location of both satellites inside their cluster to maximize the separation between them and safe the mission.

Keywords: Satellite, GEO, collocation, risk assessment.

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Authors: M. Zarebnia, R. Parvaz

Abstract:

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

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

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Authors: Khosrow Maleknejad, Reza Mollapourasl, Parvin Torabi, Mahdiyeh Alizadeh,

Abstract:

Sinc-collocation scheme is one of the new techniques used in solving numerical problems involving integral equations. This method has been shown to be a powerful numerical tool for finding fast and accurate solutions. So, in this paper, some properties of the Sinc-collocation method required for our subsequent development are given and are utilized to reduce integral equation of the first kind to some algebraic equations. Then convergence with exponential rate is proved by a theorem to guarantee applicability of numerical technique. Finally, numerical examples are included to demonstrate the validity and applicability of the technique.

Keywords: Integral equation, Fredholm type, Collocation method, Sinc approximation.

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Authors: E. N. Mathioudakis, E. P. Papadopoulou

Abstract:

The problem addressed herein is the efficient management of the Grid/Cluster intense computation involved, when the preconditioned Bi-CGSTAB Krylov method is employed for the iterative solution of the large and sparse linear system arising from the discretization of the Modified Helmholtz-Dirichlet problem by the Hermite Collocation method. Taking advantage of the Collocation ma-trix's red-black ordered structure we organize efficiently the whole computation and map it on a pipeline architecture with master-slave communication. Implementation, through MPI programming tools, is realized on a SUN V240 cluster, inter-connected through a 100Mbps and 1Gbps ethernet network,and its performance is presented by speedup measurements included.

Keywords: Collocation, Preconditioned Bi-CGSTAB, MPI, Grid and DSM Systems.

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Authors: M. Zarebnia, R. Parvaz

Abstract:

In this paper, numerical solutions of the nonlinear Benjamin-Bona-Mahony-Burgers (BBMB) equation are obtained by a method based on collocation of cubic B-splines. Applying the Von-Neumann stability analysis, the proposed method is shown to be unconditionally stable. The method is applied on some test examples, and the numerical results have been compared with the exact solutions. The L∞ and L2 in the solutions show the efficiency of the method computationally.

Keywords: Benjamin-Bona-Mahony-Burgers equation, Cubic Bspline, Collocation method, Finite difference.

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Authors: Khosrow Maleknejad, Asyieh Ebrahimzadeh

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In this paper, the numerical solution of optimal control problem (OCP) for systems governed by Volterra integro-differential (VID) equation is considered. The method is developed by means of the Legendre wavelet approximation and collocation method. The properties of Legendre wavelet together with Gaussian integration method are utilized to reduce the problem to the solution of nonlinear programming one. Some numerical examples are given to confirm the accuracy and ease of implementation of the method.

Keywords: Collocation method, Legendre wavelet, optimal control, Volterra integro-differential equation.

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Authors: Marzieh Dosti, Alireza Nazemi

Abstract:

Recently, it is found that telegraph equation is more suitable than ordinary diffusion equation in modelling reaction diffusion for such branches of sciences. In this paper, a numerical solution for the one-dimensional hyperbolic telegraph equation by using the collocation method using the septic splines is proposed. The scheme works in a similar fashion as finite difference methods. Test problems are used to validate our scheme by calculate L2-norm and L∞-norm. The accuracy of the presented method is demonstrated by two test problems. The numerical results are found to be in good agreement with the exact solutions.

Keywords: B-spline, collocation method, second-order hyperbolic telegraph equation, difference schemes.

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Authors: Yukiko Sasaki Alam

Abstract:

This research aims at finding out the causes that led to wrong lexical selections in machine translation (MT) rather than categorizing lexical errors, which has been a main practice in error analysis. By manually examining and analyzing lexical errors outputted by a MT system, it suggests what knowledge would help the system reduce lexical errors.

Keywords: Error analysis, causes of errors, machine translation, outputs evaluation.

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Authors: Mohammad ALAmro

Abstract:

The most crucial aspect that is closely related to vocabulary and the one that needs to be emphasized and investigated more than it has been up until now, is the ability to combine words that co-occur frequently in the language. Pedagogically, collocation is one of the error-provoking aspects in foreign language learning. This is indicative of the dire need to provide L2 learners with tools to help them improve their collocational knowledge. This paper pinpoints the role that collocations play in the English language. Furthermore, it presents pedagogical implications for ESL/EFL learners.

Keywords: Collocation, pedagogy, vocabulary knowledge.

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Authors: Mohammad J. Rezai, Fereshteh Davarpanah

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Producing a text in a language which is not one’s mother tongue can be a demanding task for language learners. Examining lexical errors committed by EFL learners is a challenging area of investigation which can shed light on the process of second language acquisition. Despite the considerable number of investigations into grammatical errors, few studies have tackled formal and semantic errors of lexis committed by EFL learners. The current study aimed at examining Persian learners’ formal and semantic errors of lexis in English. To this end, 60 students at three different proficiency levels were asked to write on 10 different topics in 10 separate sessions. Finally, 600 essays written by Persian EFL learners were collected, acting as the corpus of the study. An error taxonomy comprising formal and semantic errors was selected to analyze the corpus. The formal category covered misselection and misformation errors, while the semantic errors were classified into lexical, collocational and lexicogrammatical categories. Each category was further classified into subcategories depending on the identified errors. The results showed that there were 2583 errors in the corpus of 9600 words, among which, 2030 formal errors and 553 semantic errors were identified. The most frequent errors in the corpus included formal error commitment (78.6%), which were more prevalent at the advanced level (42.4%). The semantic errors (21.4%) were more frequent at the low intermediate level (40.5%). Among formal errors of lexis, the highest number of errors was devoted to misformation errors (98%), while misselection errors constituted 2% of the errors. Additionally, no significant differences were observed among the three semantic error subcategories, namely collocational, lexical choice and lexicogrammatical. The results of the study can shed light on the challenges faced by EFL learners in the second language acquisition process.

Keywords: Collocational errors, lexical errors, Persian EFL learners, semantic errors.

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Authors: Haniye Dehestani, Yadollah Ordokhani

Abstract:

In this work, we present an efficient approach for solving variable-order time-fractional partial differential equations, which are based on Legendre and Laguerre polynomials. First, we introduced the pseudo-operational matrices of integer and variable fractional order of integration by use of some properties of Riemann-Liouville fractional integral. Then, applied together with collocation method and Legendre-Laguerre functions for solving variable-order time-fractional partial differential equations. Also, an estimation of the error is presented. At last, we investigate numerical examples which arise in physics to demonstrate the accuracy of the present method. In comparison results obtained by the present method with the exact solution and the other methods reveals that the method is very effective.

Keywords: Collocation method, fractional partial differential equations, Legendre-Laguerre functions, pseudo-operational matrix of integration.

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Authors: Mehmet Ozcan

Abstract:

This study is designed to investigate errors emerged in written texts produced by 30 Turkish EFL learners with an explanatory, and thus, qualitative perspective. Erroneous language elements were identified by the researcher first and then their grammaticality and intelligibility were checked by five native speakers of English. The analysis of the data showed that it is difficult to claim that an error stems from only one single factor since different features of an error are triggered by different factors. Our findings revealed two different types of errors: those which stem from the interference of L1 with L2 and those which are developmental ones. The former type contains more global errors whereas the errors in latter type are more intelligible.

Keywords: Contrastive analysis, Error analysis, Language acquisition, Language transfer, Turkish

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Authors: A. A. Hussen, I. N. Jleta

Abstract:

Micro-electromechanical system (MEMS) accelerometers and gyroscopes are suitable for the inertial navigation system (INS) of many applications due to low price, small dimensions and light weight. The main disadvantage in a comparison with classic sensors is a worse long term stability. The estimation accuracy is mostly affected by the time-dependent growth of inertial sensor errors, especially the stochastic errors. In order to eliminate negative effects of these random errors, they must be accurately modeled. In this paper, the Allan variance technique will be used in modeling the stochastic errors of the inertial sensors. By performing a simple operation on the entire length of data, a characteristic curve is obtained whose inspection provides a systematic characterization of various random errors contained in the inertial-sensor output data.

Keywords: Allan variance, accelerometer, gyroscope, stochastic errors.

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Authors: F. Bayatbabolghani, K. Parand

Abstract:

In this paper, we propose Hermite collocation method for solving Thomas-Fermi equation that is nonlinear ordinary differential equation on semi-infinite interval. This method reduces the solution of this problem to the solution of a system of algebraic equations. We also present the comparison of this work with solution of other methods that shows the present solution is more accurate and faster convergence in this problem.

Keywords: Collocation method, Hermite function, Semi-infinite, Thomas-Fermi equation.

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Authors: Joan Goh, Ahmad Abd. Majid, Ahmad Izani Md. Ismail

Abstract:

In this paper, collocation based cubic B-spline and extended cubic uniform B-spline method are considered for solving one-dimensional heat equation with a nonlocal initial condition. Finite difference and θ-weighted scheme is used for time and space discretization respectively. The stability of the method is analyzed by the Von Neumann method. Accuracy of the methods is illustrated with an example. The numerical results are obtained and compared with the analytical solutions.

Keywords: Heat equation, Collocation based, Cubic Bspline, Extended cubic uniform B-spline.

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Authors: Ashvin Gopaul, Jayrani Cheeneebash, Kamleshsing Baurhoo

Abstract:

In this paper we study some numerical methods to solve a model one-dimensional convection–diffusion equation. The semi-discretisation of the space variable results into a system of ordinary differential equations and the solution of the latter involves the evaluation of a matrix exponent. Since the calculation of this term is computationally expensive, we study some methods based on Krylov subspace and on Restrictive Taylor series approximation respectively. We also consider the Chebyshev Pseudospectral collocation method to do the spatial discretisation and we present the numerical solution obtained by these methods.

Keywords: Chebyshev Pseudospectral collocation method, convection-diffusion equation, restrictive Taylor approximation.

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Authors: O. A. Akinfenwa, N.M. Yao, S. N. Jator

Abstract:

In this paper, a self starting two step continuous block hybrid formulae (CBHF) with four Off-step points is developed using collocation and interpolation procedures. The CBHF is then used to produce multiple numerical integrators which are of uniform order and are assembled into a single block matrix equation. These equations are simultaneously applied to provide the approximate solution for the stiff ordinary differential equations. The order of accuracy and stability of the block method is discussed and its accuracy is established numerically.

Keywords: Collocation and Interpolation, Continuous HybridBlock Formulae, Off-Step Points, Stability, Stiff ODEs.

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Authors: Mahdi Sharifian, Mohammad Ali Fanaei

Abstract:

Saccharomyces cerevisiae (baker-s yeast) can exhibit sustained oscillations during the operation in a continuous bioreactor that adversely affects its stability and productivity. Because of heterogeneous nature of cell populations, the cell population balance models can be used to capture the dynamic behavior of such cultures. In this paper an unstructured, segregated model is used which is based on population balance equation(PBE) and then in order to simulation, the 4th order Rung-Kutta is used for time dimension and three methods, finite difference, orthogonal collocation on finite elements and Galerkin finite element are used for discretization of the cell mass domain. The results indicate that the orthogonal collocation on finite element not only is able to predict the oscillating behavior of the cell culture but also needs much little time for calculations. Therefore this method is preferred in comparison with other methods. In the next step two controllers, a globally linearizing control (GLC) and a conventional proportional-integral (PI) controller are designed for controlling the total cell mass per unit volume, and performances of these controllers are compared through simulation. The results show that although the PI controller has simpler structure, the GLC has better performance.

Keywords: Bioreactor, cell population balance, finite difference, orthogonal collocation on finite elements, Galerkin finite element, feedback linearization, PI controller.

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Authors: N. M. Kamoh, D. G. Gyemang, M. C. Soomiyol

Abstract:

This paper compared the efficiency of Simpson’s 1/3 and 3/8 rules for the numerical solution of first order Volterra integro-differential equations. In developing the solution, collocation approximation method was adopted using the shifted Legendre polynomial as basis function. A block method approach is preferred to the predictor corrector method for being self-starting. Experimental results confirmed that the Simpson’s 3/8 rule is more efficient than the Simpson’s 1/3 rule.

Keywords: Collocation shifted Legendre polynomials, Simpson’s rule and Volterra integro-differential equations.

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Authors: N. Georgoulopoulos, A. Hatzopoulos, K. Karamitsios, K. Kotrotsios, A. I. Metsai

Abstract:

Current server systems are responsible for critical applications that run in different infrastructures, such as the cloud, physical machines, and virtual machines. A common challenge that these systems face are the various hardware faults that may occur due to the high load, among other reasons, which translates to errors resulting in malfunctions or even server downtime. The most important hardware parts, that are causing most of the errors, are the CPU, RAM, and the hard drive - HDD. In this work, we investigate selected CPU, RAM, and HDD errors, observed or simulated in kernel ring buffer log files from GNU/Linux servers. Moreover, a severity characterization is given for each error type. Understanding these errors is crucial for the efficient analysis of kernel logs that are usually utilized for monitoring servers and diagnosing faults. In addition, to support the previous analysis, we present possible ways of simulating hardware errors in RAM and HDD, aiming to facilitate the testing of methods for detecting and tackling the above issues in a server running on GNU/Linux.

Keywords: hardware errors, Kernel logs, GNU/Linux servers, RAM, HDD, CPU

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Authors: N. Ebrahimi, J. Rashidinia

Abstract:

In this paper, numerical solution of system of Fredholm and Volterra integral equations by means of the Spline collocation method is considered. This approximation reduces the system of integral equations to an explicit system of algebraic equations. The solution is collocated by cubic B-spline and the integrand is approximated by the Newton-Cotes formula. The error analysis of proposed numerical method is studied theoretically. The results are compared with the results obtained by other methods to illustrate the accuracy and the implementation of our method.

Keywords: Convergence analysis, Cubic B-spline, Newton- Cotes formula, System of Fredholm and Volterra integral equations.

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Authors: Marzieh Dosti, Alireza Nazemi

Abstract:

In this paper, the telegraph equation is solved numerically by cubic B-spline quasi-interpolation .We obtain the numerical scheme, by using the derivative of the quasi-interpolation to approximate the spatial derivative of the dependent variable and a low order forward difference to approximate the temporal derivative of the dependent variable. The advantage of the resulting scheme is that the algorithm is very simple so it is very easy to implement. The results of numerical experiments are presented, and are compared with analytical solutions by calculating errors L2 and L∞ norms to confirm the good accuracy of the presented scheme.

Keywords: Cubic B-spline, quasi-interpolation, collocation method, second-order hyperbolic telegraph equation.

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Authors: Yung-Yuan Chen, Kuen-Long Leu

Abstract:

FlexRay, as a communication protocol for automotive control systems, is developed to fulfill the increasing demand on the electronic control units for implementing systems with higher safety and more comfort. In this work, we study the impact of radiation-induced soft errors on FlexRay-based steer-by-wire system. We injected the soft errors into general purpose register set of FlexRay nodes to identify the most critical registers, the failure modes of the steer-by-wire system, and measure the probability distribution of failure modes when an error occurs in the register file.

Keywords: Soft errors, FlexRay, fault injection, steer-by-wirer

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Authors: Zayed N. Alsulami, Asma F. Aldosseri, Ahmed S. Ezziden, Abdulrahman K. Alonazi

Abstract:

Children are more susceptible to medication errors than adults. Medication administration process is the last stage in the medication treatment process and most of the errors detected in this stage. Little research has been undertaken about medication errors in children in the Middle East countries. This study was aimed to evaluate how the paediatric nurses adhere to the medication administration policy and also to identify any medication preparation and administration errors or any risk factors. An observational, prospective study of medication administration process from when the nurses preparing patient medication until administration stage (May to August 2014) was conducted in Saudi Arabia. Twelve paediatric nurses serving 90 paediatric patients were observed. 456 drug administered doses were evaluated. Adherence rate was variable in 7 steps out of 16 steps. Patient allergy information, dose calculation, drug expiry date were the steps in medication administration with lowest adherence rates. 63 medication preparation and administration errors were identified with error rate 13.8% of medication administrations. No potentially life-threating errors were witnessed. Few logistic and administrative factors were reported. The results showed that the medication administration policy and procedure need an urgent revision to be more sensible for nurses in practice. Nurses’ knowledge and skills regarding to the medication administration process should be improved.

Keywords: Double checking, Medication administration errors, Medication safety, Nurses.

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Authors: A. A. James, A. O. Adesanya, M. R. Odekunle, D. G. Yakubu

Abstract:

This paper examines the development of one step, five hybrid point method for the solution of first order initial value problems. We adopted the method of collocation and interpolation of power series approximate solution to generate a continuous linear multistep method. The continuous linear multistep method was evaluated at selected grid points to give the discrete linear multistep method. The method was implemented using a constant order predictor of order seven over an overlapping interval. The basic properties of the derived corrector was investigated and found to be zero stable, consistent and convergent. The region of absolute stability was also investigated. The method was tested on some numerical experiments and found to compete favorably with the existing methods.

Keywords: Interpolation, Approximate Solution, Collocation, Differential system, Half step, Converges, Block method, Efficiency.

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Authors: Shazalina Mat Zin, Ahmad Abd. Majid, Ahmad Izani Md. Ismail, Muhammad Abbas

Abstract:

The generalized wave equation models various problems in sciences and engineering. In this paper, a new three-time level implicit approach based on cubic trigonometric B-spline for the approximate solution of wave equation is developed. The usual finite difference approach is used to discretize the time derivative while cubic trigonometric B-spline is applied as an interpolating function in the space dimension. Von Neumann stability analysis is used to analyze the proposed method. Two problems are discussed to exhibit the feasibility and capability of the method. The absolute errors and maximum error are computed to assess the performance of the proposed method. The results were found to be in good agreement with known solutions and with existing schemes in literature.

Keywords: Collocation method, Cubic trigonometric B-spline, Finite difference, Wave equation.

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Authors: Yukiko Sasaki Alam, Shahid Alam

Abstract:

Syntactic parsing is vital for semantic treatment by many applications related to natural language processing (NLP), because form and content coincide in many cases. However, it has not yet reached the levels of reliable performance. By manually examining and analyzing individual machine translation output errors that involve syntax as well as semantics, this study attempts to discover what is required for improving syntactic and semantic parsing.

Keywords: Machine translation, error analysis, syntactic errors, knowledge required for parsing.

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