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.
Abstract: The purpose of this paper is to propose a text mining
approach to evaluate companies- practices on affective management.
Affective management argues that it is critical to take stakeholders-
affects into consideration during decision-making process, along with
the traditional numerical and rational indices. CSR reports published
by companies were collected as source information. Indices were
proposed based on the frequency and collocation of words relevant to
affective management concept using text mining approach to analyze
the text information of CSR reports. In addition, the relationships
between the results obtained using proposed indices and traditional
indicators of business performance were investigated using
correlation analysis. Those correlations were also compared between
manufacturing and non-manufacturing companies. The results of this
study revealed the possibility to evaluate affective management
practices of companies based on publicly available text documents.
Abstract: A generalized Dirichlet to Neumann map is
one of the main aspects characterizing a recently introduced
method for analyzing linear elliptic PDEs, through which it
became possible to couple known and unknown components
of the solution on the boundary of the domain without
solving on its interior. For its numerical solution, a well conditioned
quadratically convergent sine-Collocation method
was developed, which yielded a linear system of equations
with the diagonal blocks of its associated coefficient matrix
being point diagonal. This structural property, among others,
initiated interest for the employment of iterative methods for
its solution. In this work we present a conclusive numerical
study for the behavior of classical (Jacobi and Gauss-Seidel)
and Krylov subspace (GMRES and Bi-CGSTAB) iterative
methods when they are applied for the solution of the Dirichlet
to Neumann map associated with the Laplace-s equation
on regular polygons with the same boundary conditions on
all edges.
Abstract: Through inward perceptions, we intuitively expect
distributed software development to increase the risks associated with
achieving cost, schedule, and quality goals. To compound this
problem, agile software development (ASD) insists one of the main
ingredients of its success is cohesive communication attributed to
collocation of the development team. The following study identified
the degree of communication richness needed to achieve comparable
software quality (reduce pre-release defects) between distributed and
collocated teams. This paper explores the relevancy of
communication richness in various development phases and its
impact on quality. Through examination of a large distributed agile
development project, this investigation seeks to understand the levels
of communication required within each ASD phase to produce
comparable quality results achieved by collocated teams. Obviously,
a multitude of factors affects the outcome of software projects.
However, within distributed agile software development teams, the
mode of communication is one of the critical components required to
achieve team cohesiveness and effectiveness. As such, this study
constructs a distributed agile communication model (DAC-M) for
potential application to similar distributed agile development efforts
using the measurement of the suitable level of communication. The
results of the study show that less rich communication methods, in
the appropriate phase, might be satisfactory to achieve equivalent
quality in distributed ASD efforts.
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.
Abstract: Selecting the word translation from a set of target
language words, one that conveys the correct sense of source word
and makes more fluent target language output, is one of core
problems in machine translation. In this paper we compare the 3
methods of estimating word translation probabilities for selecting the
translation word in Thai – English Machine Translation. The 3
methods are (1) Method based on frequency of word translation, (2)
Method based on collocation of word translation, and (3) Method
based on Expectation Maximization (EM) algorithm. For evaluation
we used Thai – English parallel sentences generated by NECTEC.
The method based on EM algorithm is the best method in comparison
to the other methods and gives the satisfying results.
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.
Abstract: This paper study the behavior of the solution at the crack edges for an elliptical crack with developing cusps, Ω in the plane elasticity subjected to shear loading. The problem of finding the resulting shear stress can be formulated as a hypersingular integral equation over Ω and it is then transformed into a similar equation over a circular region, D, using conformal mapping. An appropriate collocation points are chosen on the region D to reduce the hypersingular integral equation into a system of linear equations with (2N+1)(N+1) unknown coefficients, which will later be used in the determination of shear stress intensity factors and maximum shear stress intensity. Numerical solution for the considered problem are compared with the existing asymptotic solution, and displayed graphically. Our results give a very good agreement to the existing asymptotic solutions.
Abstract: In this work, are discussed two formulations of the boundary element method - BEM to perform linear bending analysis of plates reinforced by beams. Both formulations are based on the Kirchhoff's hypothesis and they are obtained from the reciprocity theorem applied to zoned plates, where each sub-region defines a beam or a slab. In the first model the problem values are defined along the interfaces and the external boundary. Then, in order to reduce the number of degrees of freedom kinematics hypothesis are assumed along the beam cross section, leading to a second formulation where the collocation points are defined along the beam skeleton, instead of being placed on interfaces. On these formulations no approximation of the generalized forces along the interface is required. Moreover, compatibility and equilibrium conditions along the interface are automatically imposed by the integral equation. Thus, these formulations require less approximation and the total number of the degree s of freedom is reduced. In the numerical examples are discussed the differences between these two BEM formulations, comparing as well the results to a well-known finite element code.
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.
Abstract: This article presents a numerical study of the doublediffusive
mixed convection in a vertical channel filled with porous
medium by using non-equilibrium model. The flow is assumed
fully developed, uni-directional and steady state. The controlling
parameters are thermal Rayleigh number (RaT ), Darcy number (Da),
Forchheimer number (F), buoyancy ratio (N), inter phase heat transfer
coefficient (H), and porosity scaled thermal conductivity ratio
(γ). The Brinkman-extended non-Darcy model is considered. The
governing equations are solved by spectral collocation method. The
main emphasize is given on flow profiles as well as heat and solute
transfer rates, when two diffusive components in terms of buoyancy
ratio are in favor (against) of each other and solid matrix and fluid
are thermally non-equilibrium. The results show that, for aiding flow
(RaT = 1000), the heat transfer rate of fluid (Nuf ) increases upto a
certain value of H, beyond that decreases smoothly and converges
to a constant, whereas in case of opposing flow (RaT = -1000),
the result is same for N = 0 and 1. The variation of Nuf in (N,
Nuf )-plane shows sinusoidal pattern for RaT = -1000. For both cases
(aiding and opposing) the flow destabilize on increasing N by inviting
point of inflection or flow separation on the velocity profile. Overall,
the buoyancy force have significant impact on the non-Darcy mixed
convection under LTNE conditions.
Abstract: Term Extraction, a key data preparation step in Text
Mining, extracts the terms, i.e. relevant collocation of words,
attached to specific concepts (e.g. genetic-algorithms and decisiontrees
are terms associated to the concept “Machine Learning" ). In
this paper, the task of extracting interesting collocations is achieved
through a supervised learning algorithm, exploiting a few
collocations manually labelled as interesting/not interesting. From
these examples, the ROGER algorithm learns a numerical function,
inducing some ranking on the collocations. This ranking is optimized
using genetic algorithms, maximizing the trade-off between the false
positive and true positive rates (Area Under the ROC curve). This
approach uses a particular representation for the word collocations,
namely the vector of values corresponding to the standard statistical
interestingness measures attached to this collocation. As this
representation is general (over corpora and natural languages),
generality tests were performed by experimenting the ranking
function learned from an English corpus in Biology, onto a French
corpus of Curriculum Vitae, and vice versa, showing a good
robustness of the approaches compared to the state-of-the-art Support
Vector Machine (SVM).
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.
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.
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.
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.
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.
Abstract: We consider the development of an eight order Adam-s
type method, with A-stability property discussed by expressing them
as a one-step method in higher dimension. This makes it suitable
for solving variety of initial-value problems. The main method and
additional methods are obtained from the same continuous scheme
derived via interpolation and collocation procedures. The methods
are then applied in block form as simultaneous numerical integrators
over non-overlapping intervals. Numerical results obtained using the
proposed block form reveals that it is highly competitive with existing
methods in the literature.
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.
Abstract: In this paper we use quintic non-polynomial
spline functions to develop numerical methods for approximation
to the solution of a system of fourth-order boundaryvalue
problems associated with obstacle, unilateral and contact
problems. The convergence analysis of the methods has been
discussed and shown that the given approximations are better
than collocation and finite difference methods. Numerical
examples are presented to illustrate the applications of these
methods, and to compare the computed results with other
known methods.