• 作者： 林真真
• 作者服務機構： 銘傳管理學院統計系
• 中文摘要： 本文旨在探討具震盪核的漢克轉換，並導得一精確的數值方法來計算這一類的積分。吾人應用阿貝爾轉換及梭寧積分公式將複雜的漢克轉換轉化成遠為簡單的基本函數的積分。後者將以調適費朗積分法及辛普森法來作精確計算。在反算漢克轉換時，吾人以乘積積分法的技巧作半解析性的積分以避免阿貝爾轉換所涉及的奇異性。本文亦作了詳盡的誤差分析，並以數個數值例子計算的結果佐證了本文數值辦法之精確性。
• 英文摘要： In this paper, we consider Hankel transforms with oscillatory kernels and derive an accurate numericalalgorithm for these integrals. It is shown that the Abel transform and Sonine's integral can be employedto transform Hankel transforms to those involving elementary oscillatory functions, which are then handledby employing an adaptive Filon's quadrature together with Simpson's method. In recovering the Hankeltransforms, the technique of product integration is used to avoid the singularity of the inverse Abeltransform. Error analysis is carefully done, and numerical examples are presented to demonstrate theaccuracy of the numerical algorithm.
• 中文關鍵字： Abel transform; adaptive Filon's method; product integration; error analysis
• 英文關鍵字： --