Numerical Quadrature for Bessel Transformations with High Oscillations

Authors:
Shuhuang Xiang
Affiliations:
Central South University, Changsha, Hunan, China 410083
Venue:
Numerical Analysis and Its Applications
Year:
2009

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Abstract

We explore higher order numerical quadrature for the integration of systems containing Bessel functions such as $\int_a^b f(x)J_{\nu}(rx)dx$ and $\int_a^b f(x)\cos(r_1x)J_{\nu}(rx)dx$. The decay of the error of the these methods drastically improves as frequency grows.