In this paper, we develop spline collocation technique for the numerical solution of
general twelfth-order linear boundary value problems (BVPs). This technique based on
polynomial splines from order sixteenth as well as five collocation points at
every
subinterval of BVPs. The method developed not only approximates the solution of BVP,
but its higher order derivatives as well. We show that the spline collocation method is
existent and unique when it is applied into a test problem. Also, its global truncation error
is estimated. Moreover, the purposed spline method when applied to test problems will be
consistent and convergent from sixteenth order. Three numerical examples are given to
illustrate the applicability and efficiency of the new method. Comparisons of our results
with some other methods show that our method is very effective and successful.
In this paper, spline technique with five collocation parameters for finding the
numerical solutions of delay differential equations (DDEs) is introduced. The presented
method is based on the approximating the exact solution by C4-Hermite spline
i
nterpolation and as well as five collocation points at every subinterval of DDE.The study
shows that the spline solution of purposed technique is existent and unique and has
strongly stable for some collocation parameters. Moreover, this method if applied to test
problem will be consistent, p-stable and convergent from order nine .In addition ,it
possesses unbounded region of p-stability. Numerical experiments for four examples are
given to verify the reliability and efficiency of the purposed technique. Comparisons show
that numerical results of our method are more accurate than other methods.
In this paper, spline approximations with five collocation points are used for the
numerical simulation of stochastic of differential equations(SDE). First, we have modeled
continuous-valued discrete wiener process, and then numerical asymptotic st
ochastic
stability of spline method is studied when applied to SDEs. The study shows that the
method when applied to linear and nonlinear SDEs are stable and convergent.
Moreover, the scheme is tested on two linear and nonlinear problems to illustrate
the applicability and efficiency of the purposed method. Comparisons of our results with
Euler–Maruyama method, Milstein’s method and Runge-Kutta method, it reveals that the
our scheme is better than others.
In this paper, an iterative numerical method for obtaining approximate values of
definite single, double and triple integrals will be illustrated. This method depends on
approximating the single integral function by spline polynomial of fifth degre
e, while
Gauss Legendre points as well as spline polynomials are used for finding multiple
integrals.
The study shows that when the method are applied to single integrals is convergent
of order sixth, as well as when applied to triple integrals is convergent of order sixth for
three Gauss Legendre points or greater.
Errors estimates of the proposed method alongside numerical examples are given to
test the convergence and accuracy of the method.
In this paper, we use polynomial splines of eleventh degree with three collocation
points to develop a method for computing approximations to the solution and its
derivatives up to ninth order for general linear and nonlinear ninth-order boundary-v
alue
problems (BVPs). The study shows that the spline method with three collocation points
when is applied to these problems is existent and unique. We prove that the proposed
method if applied to ninth-order BVPs is stable and consistent of order eleven, and it
possesses convergence rate greater than six.
Finally, some numerical experiments are presented for illustrating the theoretical
results and by comparing the results of our method with the other methods, we reveal that
the proposed method is better than others.
The extended text, that contains much paragraphs, is built on parts. These are
phrases, clauses, sentences.
Text,s linguists try to pass sentence for the whole of text, but they don,t ignore considering
that a sentence is the basis of analysis and
interpretation.
Collocations are a"micro semantic units" in a text, but grammatically they are sentences,
phrases, or clauses. These structures are able to give the macro semantic units,
which the producer intends to show to the receiver by several manners, or process, whereas,
part refers to whole.
Collocations may be a nucler topic storing the text,s macro semantic units, in one
part, or contain correlating " themes" to reffier to it, in second part, or include connotations
united to reffier to it, in third part.
R.Barthes declared that producer is dead, and J.Kristiva said that text is opened , so
receiver contributes in reproducing, according to his cultural background, knowledge of
the world, and experiences.
Our Study depended on "voice,scollocations", and its role in "Coherence" in Narrative
Text:( Ghadah al-Samman,s "Beirut 75").
In this paper, a spline collocation method is developed for finding numerical solutions of general linear eighth-order boundary-value problems (BVPs) and nonlinear eighth-order initial value problems (IVPs). The presented collocation method affords t
he spline solution by the polynomial of degree eleventh which satisfies the BVPs and IVPs at three collocation points. The study shows that the spline collocation method when is applied such this problems is existent and unique. Moreover, the purposed method if applied to these systems will be consistent and the global truncation error equal eleventh.
Numerical results are given for four examples to illustrate the implementation and efficiency of the method. Comparisons of the results obtained by the present method with results obtained by the other methods reveal that the present method is very effective and convenient.
In this paper, we introduce a numerical method for solving systems of high-index differential algebraic equations. This method is based on approximating the exact solution by spline polynomial of degree eight with five collocation points to find the
numerical solution in each step. The study shows that the method when applied to linear differential-algebraic systems with index equal one is stable and convergent of order 8, while it is stable and convergent of order 9-u for index equal u .
Numerical experiments for four test examples and comparisons with other available results are given to illustrate the applicability and efficiency of the presented method
This piece of research endeavours to highlight the inevitability of the
micro-textonymic transformations throughout the process of translation. The claim that translation necessitates transformation has been ascertained through rendering a few non/
conventional micro-textonymic English collocational patterns into Arabic. However, though some translation theorists comprehend transformations as a remark of inescapable weakness, others maintain its prominence in successfully communicating the TL recipients, to the extent that there is no transation without transformation. Translator's skilfulness and expertise would closely monitor and manage such micro-textonymic transformations, being the decoder of the ST and re-encoder of the TT. Faithfulness in translation has been defined not in relation to extremely possible literalism and adherence to the ST, rather, it stands as a remark of how far do such micro-textonymic transformations help translators communicate the rhetoric of the ST, and guarantee acceptance and readability in the TL language and culture.
In this paper, spline collocation method is considered for solving two forms of problems. The first form is general linear sixth-order boundary-value problem (BVP), and the second form is nonlinear sixth-order initial value problem (IVP). The existen
ce, uniqueness, error estimation and convergence analysis of purpose methods are investigated. The study shows that proposed spline method with three collocation points can find the spline solutions and their derivatives up to sixth-order of the two BVP and IVP, thus is very effective tools in numerically solving such problems. Several examples are given to verify the reliability and efficiency of the proposed method. Comparisons are made to reconfirm the efficiency and accuracy of the suggested techniques.
