The working up of the training informational module: ″The methods of the approximate calculation of double integrals″
Khomchenko A.N., Tuluchenko G.Ya.
Kherson State Technical University
The report contains the descriptions of the alternative cubature formulas and the experience of the informational module using in the study process that is directed at the study of the approximate calculation methods of double integrals.
The tendency of hours cutting down for study of the higher and applied mathematics in the higher technical educational institutions that is observed in Ukraine at the last years prompts the lecturers of these disciplines to search persistently for the ways to intensify the educational process. The recognized way is the using of object-competent informational module. They allow showing the students of engineering specialties the modern methods of the mathematical modeling. Among this methods the method of finite elements takes the prominent place.
At its realization the operation of the approximate calculation of divisible integrals on the spheres of finite elements plays the important part. That’s why much attention is paid now to construction of the alternative cubature formulas. Their existence is confirmed by the presence of alternative bases for same finite elements. Often the quality of cubature formulas is conditioned by properties of underintegral function. That’s why teaching the students of the engineering specialties to methods of choosing the cubature formula depending on the contents of the applied problem is expedient.
The creating of library of alternative cubature formulas for different kinds of finite elements with different knots quantity was begun in the works of A.N.Khomchenko and his pupils. The authors have received alternative cubature formulas by weighed meaning method for centralized triangle complex-element with ten knots (picture 1):
where D – the triangle complex-element, - this element area, - values of function in element knots .
The spectrum of weight coefficients for cubature formula (1) has been repeated at fractions random walks modeling within the limits of finite element with the absorb knots. With the help of the informational module the series of experiments for estimation of exactness of formula (1) have been made.
|Kravtsov H. M. The Kherson State University||Fedorchenko K. A. Kherson State University, Ukraine|
|D. Е. Schedrolosiev Kherson State University, Ukraine||D. Е. Schedrolosiev Kherson State University, Ukraine|
|Kravtsov D. H. The Kherson State University, Ukraine||K. R. Allayev g. M. Fedorenko tashkent State Technical University V. I. Postnikov uzbekistan L. B. Ostapchuk|
|Homchenko A. N., Valko N. V., Letvinenko O. I. The Kherson state university|
Р, and also double integrals on volume of a sphere. Besides the vicinity of point р not necessarily should be circle or a sphere
|Spivakovsky О. V. Kherson State University, Ukraine|
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