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.
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Xiang, S. (2009). Numerical Quadrature for Bessel Transformations with High Oscillations. In: Margenov, S., Vulkov, L.G., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2008. Lecture Notes in Computer Science, vol 5434. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00464-3_69
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DOI: https://doi.org/10.1007/978-3-642-00464-3_69
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