Supervisors info:
Σωτήριος Ε. Νοτάρης, καθηγητής, Τμήμα Μαθηματικών, Σ.Θ.Ε., Ε.Κ.Π.Α.
Βασίλειος Δουγαλής, ομότιμος καθηγητής, Τμήμα Μαθηματικών, Σ.Θ.Ε., Ε.Κ.Π.Α.
Μιχάλης Δρακόπουλος, επίκουρος καθηγητής, Τμήμα Μαθηματικών, Σ.Θ.Ε., Ε.Κ.Π.Α.
Summary:
The theme of the work, as indicated by its title, is the numerical integration, ie, the estimated price of a certain integral with a numerical method. The numerical integration is a classic issue of numerical analysis and its utility New is two main reasons: If f is the function we conclude, then a factor of F can be determined only analytically in rare cases, and even when it is feasible, the calculation of F can be disadvantageous. For, if possible, better presentation of the concepts we are studying, the work is divided into four chapters, where:
In the first chapter we introduce the concept of orthogonal polynomials noting their basic properties, such as the retro type, the properties of their roots, the Christoffel-Darboux identity and then the Chebyshev polynomials of the first and second kind.
In the second chapter we present basic numerical integration elements: Types numerical integration interpolated, the degree of accuracy, convergence of these types of functions for different classes and their error, by methods Hilbert spaces, for analytic functions.
In the third chapter we study four specific types of numerical integration interpolated: They called Fejer types of first and second type, the type of Basu and type of Clenshaw-Curtis, looking for everyone matters analyzed in the third chapter.
In the fourth chapter we move to some numerical examples. Specifically, we estimate the error of the type studied in the third chapter of a series of functions, we approach the integral of a function that shows an anomaly at one end of the integration period, and finally we find bounds for the error type of Fejer second type for analytic functions.
Keywords:
Chebyshev, Fejer, Basu, Clenshaw, Curtis
