University of Tasmania
whole_DonaldsonJohnDalgleish1968_thesis.pdf (6.68 MB)

Asymptotic estimates of the errors in the numerical integration of analytic functions

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posted on 2023-05-26, 20:05 authored by Donaldson, John Dalgleish
An expression in terms of a contour integral for the remainder term in a numerical integration formula of a general type is obtained. Because the function whose integral is under consideration is allowed to have singularities at the end points of the interval of integration special emphasis is placed on the behaviour of the contour at these points. It is then shown how the corresponding contour integral form of the remainder term in some of the well-known integration formulae may be derived. The contour integral in conjunction with known asymptotic expressions for part of the integrand is used firstly to examine the convergence properties of certain quadrature schemes (Chapter III) and secondly to estimate the error in approximating to a real integral by a quadrature sum (Chapter IV). In conclusion (Chapter V) we discuss some of the problems which are to be subjects of further research.


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Copyright 1967 the Author - The University is continuing to endeavour to trace the copyright owner(s) and in the meantime this item has been reproduced here in good faith. We would be pleased to hear from the copyright owner(s). Includes bibliography

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  • Open

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