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<p>This study introduces new methods for approximating the infinite integrals containing the exponential and Bessel functions with large parameters. The analysis begins by deriving the analytical expressions for the relevant moments and establishing their asymptotic orders. Based on these results, two schemes are introduced: an asymptotic method and a Filon-type method. These proposed techniques are then validated through a series of numerical experiments, which confirm their effectiveness and support the theoretical findings.</p>

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Moments-based computation of highly oscillatory integrals with exponential and Bessel kernels

  • 期刊论文

  • 发表日期：

    2026年7月3日

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  • Ruyun Chen,
  • Hong Du

摘要

This study introduces new methods for approximating the infinite integrals containing the exponential and Bessel functions with large parameters. The analysis begins by deriving the analytical expressions for the relevant moments and establishing their asymptotic orders. Based on these results, two schemes are introduced: an asymptotic method and a Filon-type method. These proposed techniques are then validated through a series of numerical experiments, which confirm their effectiveness and support the theoretical findings.