The fluctuationlessness approach to the numerical integration of functions with a single variable by integrating Taylor expansion with explicit remainder term

In this paper we give the definition of the Fluctuationlessness concept and using this concept we make approximations to univariate functions by using Taylor expansion with the explicit remainder term. Then integrating this approximate expression we obtain a new quadrature-like numerical integration...

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Bibliographic Details
Published in:Journal of mathematical chemistry 2011-02, Vol.49 (2), p.393-406
Main Authors: Baykara, N. A., Gürvit, Ercan, Demiralp, Metin
Format: Article
Language:English
Subjects:
Approximations and expansions
Chemistry
Chemistry and Materials Science
Exact sciences and technology
Functions of a complex variable
General and physical chemistry
Math. Applications in Chemistry
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical approximation
Original Paper
Physical Chemistry
Sciences and techniques of general use
Theoretical and Computational Chemistry
Theory of reactions, general kinetics. Catalysis. Nomenclature, chemical documentation, computer chemistry
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Summary:In this paper we give the definition of the Fluctuationlessness concept and using this concept we make approximations to univariate functions by using Taylor expansion with the explicit remainder term. Then integrating this approximate expression we obtain a new quadrature-like numerical integration method. The results of numerical experiments are compared with the results obtained from the corresponding Taylor series expansion without the remainder term and errors are analyzed.
ISSN:0259-9791
1572-8897
DOI:10.1007/s10910-010-9748-5