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International Conference on Statistics, Combinatorics and Related Areas and the Eighth International Conference of Forum for Interdisciplinary Mathematics
December 19-21, 2001
School of Mathematics and Applied Statistics, University of Wollongong
Wollongong, NSW, Australia

Organizers
Satya N. Mishra (University of South Alabama), Chandra M. Gulati (University of Wollongong)

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Approximating the Cauchy Principal Value Integral Via Hermite-Hadamard Type Inequalities
by
Sever S. Dragomir
Victoria University, Melbourne, Victoria, Australia

Numerical evaluation of the Cauchy principal value (CPV) integral, is encountered in many areas of Applied Mathematics such as the crack problems in plane elasticity, the singular eigenfunction method in neutron transport, in airfoil theory, in electromagnetic scattering in waveform encoding of binary signals, in visualization of cardiovascular velocity maps and in demultiplexing of interferometrically interrogated fiber Bragg Gratings etc. In the present paper, by the use of Hermite-Hadamard inequality for convex functions, we establish some error bounds for the approximation of the CPV integral of a differentiable function whose derivative is convex. Some numerical experiments are performed as well.

http://rgmia.vu.edu.au/SSDragomirWeb.html

Date received: September 13, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cagd-82.