New approximation algorithm for generalized function and its its application to numerical computation

• Project/Area Number: 24540122
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Kyoto University
• Principal Investigator: Ooura Takuya 京都大学, 数理解析研究所, 助教 (50324710)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Project Status: Completed (Fiscal Year 2015)
• Budget Amount: ¥5,200,000 (Direct Cost: ¥4,000,000、Indirect Cost: ¥1,200,000); Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2012: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
• Keywords: 数値解析 / 超関数 / 連続Euler変換 / 数値計算法 / 数値積分 / 近似計算

Outline of Final Research Achievements

We propose new numerical computation methods which are derived from approximation of generalized function. Targets of computation are complicated oscillatory integral, multidimensional oscillatory integral, integral transform and fractional differential equations. New methods can be computed with high speed and high accuracy about oscillatory integrals in particular.

Research Products

• [Journal Article] Fast computation of Goursat's infinite integral with very high accuracy (2013)
  • Author(s): T. Ooura
  • Journal Title: . Comput. Appl. Math. Volume: 249 Pages: 1-8
  • DOI: 10.1016/j.cam.2013.02.006
  • NAID: 120005244245
  • Peer Reviewed
• [Journal Article] Fast computation of Goursat's infinite integral with very high accuracy (2013)
  • Author(s): T. Ooura
  • Journal Title: Journal of Computational and Applied Mathematics Volume: 249 Pages: 1-8
  • NAID: 120005244245
  • Peer Reviewed
• [Journal Article] Direct computation of generalized functions by continuous Euler transformation (2012)
  • Author(s): T. Ooura
  • Journal Title: Sugaku Expositions Volume: 25 Pages: 89-104
  • NAID: 10026415315
  • Peer Reviewed
• [Presentation] Computation of an Infinite Integral with Unbounded Integrand (2015)
  • Author(s): T. Ooura
  • Organizer: The 8th International Congress on Industrial and Applied Mathematics
  • Place of Presentation: China National Convention Center inside the Beijing Olympic Green (China)
  • Year and Date: 2015-08-10
  • Int'l Joint Research
• [Presentation] 振動積分の数値計算法について (2012)
  • Author(s): 大浦拓哉
  • Organizer: 応用数学合同研究集会
  • Place of Presentation: 龍谷大学瀬田キャンパス
  • Invited
• [Presentation] 連続オイラー変換による振動積分の算法
  • Author(s): 大浦拓哉
  • Organizer: 第42回数値解析シンポジウム
  • Place of Presentation: 松山道後温泉 道後館
  • Invited
• [Remarks] Ooura's Mathematical Software Packages
  • URL: http://www.kurims.kyoto-u.ac.jp/~ooura/index-j.html
• [Remarks] Ooura's Mathematical Software Packages
  • URL: http://www.kurims.kyoto-u.ac.jp/~ooura/index-j.html