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 work, we have studied the issue of approximation of functions from Morrey
space ; by rational functions on a large group of curves,
which called Dini-smooth curves. Moreover, approximation of functions from Morrey
Smirnov space defined on a finite domain with a boundary belonging to Dini- smooth
curves by polynomials is obtained.
The geometric correction of remote sensing images becomes a key issue in
production and updating digital maps, multisource data integration, management and
analysis for many geomatic applications. 2D polynomial functions are the most prevalent
to
achieve this correction.
Previous researches have shown that the application of 2D polynomials is
conditioned by the planarity of the terrain and the uniform distribution of ground control
points, but did not explicitly discuss the criteria for evaluating the success or failure of
their application. In this study, we will try to give some of these criteria and to develop
some old analog cartographic rules to suit the nature of the digital satellite images.
In this research, we discussed mathematical foundation for evaluating the precision
of control points- based geometric correction of satellite images. We have also tested the
effect of the topography of the imaged scene on this accuracy. The test has been carried out
by the use of satellite images extracted from Google Earth. These images cover some areas
in the city of Latakia in Syria. Also, control points have been extracted from Google Earth
and transformed into the Syrian stereographic coordinates system.
Results demonstrated that the second degree 2D polynomial is very suitable for plan
small scenes with uniform distribution of the control points over the entire scene.
Grobner Bases(GB) are considered as one of the new
mathematical tools that motivate the researchers in all
mathematical domains.They use in solving many of mathematical
problems. A Grobner basis is a set of multivariate polynomials that
has desir
able algorithmic properties. Every set of polynomials can
be transformed into a Grobner basis.
In this research, we have studied the issue of approximation of complex functions from weighted Lebesgue space ; and (Mukenhoupt weight) to rational functions by using p- Faber polynomials on large group of curves, which called Carlson curves. This
is also considered as a follow-up to the work done by researchers: Israfilov and Testici in 2014 , where they studied approximation of functions from weighted Smirnov space on domains with a Carlson curve boundary.
We study in this research approximation of complex functions from Orlicz space on a subclass of Carlson curves, which called Dini smooth curves to rational functions by using polynomials related with Dzjadyk sums which obtained from Faber polynomials. We depend on some concepts of complex analysis such as formulas of Sokhotski to reach the desired goal
