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Far East Journal of Applied Mathematics

Far East Journal of Applied Mathematics
Volume 67, Issue 1, Pages 13 - 25 (June 2012)

EXTENDING THE ISERLES-NÃ˜RSETT-FILON TYPE METHOD TO THE QUADRATURE OF CAUCHY PRINCIPAL VALUE INTEGRALS OF OSCILLATORY KIND
G. E. Okecha

Abstract:

Two methods are derived for the numerical evaluation of singular integrals of Cauchy-type, which are oscillatory. The first of the methods is based on the asymptotic expansion of the inverse of the frequency w, whilst the second is essentially an interpolatory method on a set of carefully selected knots. Proof of convergence is established and a set of two results is presented to validate the methods developed.

Keywords and phrases: numerical quadrature, high oscillation, Cauchy principal value (cpv), Hermite interpolation.

Number of Downloads: 290 | Number of Views: 962

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