Date of Publication :8th September 2024

Abstract: This paper focuses on the approximate evaluation of Cauchy-type oscillatory singular integrals of the form ∫(eiwz/z − τ)φ(z)dz;w ∈ R,|w| > 1; L where L is a directed line segment in the complex plane C joining from τ − l to τ + l; τ ∈ C is fixed. A Gauss-type quadrature rule is proposed for the approximate evaluation of line integrals ∫L φ(z)dz. Furthermore, a comprehensive scheme is developed for evaluating the Cauchy-type integrals, with error bounds established and validated through numerical experiments on various reference integrals.

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