Authors:
Umesha V.,B. K. Divyashree,S. Padmanabhan,DOI NO:
https://doi.org/10.26782/jmcms.2026.09.00009Keywords:
Highly oscillatory integrals,Genocchi wavelets,singular oscillations,numerical integration,adaptive resolution.,Abstract
This study introduces an efficient high-order wavelet quadrature technique for computing highly oscillatory integrals affected by endpoint singular behavior of the form: $latex \int_{0}^{1} f(x)\sin \left(\frac{\omega}{x^r}\right) dx \text{ and } \int_{0}^{1} f(x)\cos \left(\frac{\omega}{x^r}\right) dx, \omega \gg 1, r > 0,$ where standard numerical methods often lose stability and accuracy due to infinite oscillation frequency as x?0^+. The method applies sixth-order Genocchi wavelets within a multiresolution structure to approximate the smooth component of the integrand, while the singular boundary region is treated separately using analytical asymptotic approximations and interval decomposition. Closed-form expressions for the oscillatory kernels are obtained through appropriate transformations. Tests on several benchmark examples demonstrate very high precision, with errors ranging from 10^(-9)to 10^(-13), and show clear improvements in both accuracy and efficiency compared to existing wavelet and hybrid approaches. A practical application to radar cross-section computation is presented.Refference:
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