New conformal map for the trapezoidal formula for infinite integrals of unilateral rapidly decreasing functions

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:389

Article

Okayama, Tomoaki¹  Nomura, Tomoki²  Tsuruta, Saki³ 

[1] Hiroshima City Univ, Grad Sch Informat Sci, Asaminami Ku, 3-4-1 Ozuka Higashi, Hiroshima 7313194, Japan

[2] Hitachi Informat Engn Ltd, Naka Ku, Hiroshima K Bldg 7F,6-13 Nakamachi, Hiroshima 7300037, Japan

[3] Hiroshima Municipal Funairi High Sch, Naka Ku, 1-4-4 Funairi Minami, Hiroshima 7300847, Japan

关键词: Trapezoidal formula;    Conformal map;    Computable error bound;   

DOI  :  10.1016/j.cam.2020.113354

来源: Elsevier

【 摘 要 】

While the trapezoidal formula can attain exponential convergence when applied to infinite integrals of bilateral rapidly decreasing functions, it is not capable of this in the case of unilateral rapidly decreasing functions. To address this issue, Stenger proposed the application of a conformal map to the integrand such that it transforms into bilateral rapidly decreasing functions. Okayama and Hanada modified the conformal map and provided a rigorous error bound for the modified formula. This paper proposes a further improved conformal map, with two rigorous error bounds provided for the improved formula. Numerical examples comparing the proposed and existing formulas are also given. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free