A fourth order product integration rule by using the generalized Euler-Maclaurin summation formula

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:335

Article

Rzadkowski, Grzegorz¹  Tohidi, Emran² 

[1] Warsaw Univ Technol, Dept Finance & Risk Management, Narbutta 85, PL-02524 Warsaw, Poland

[2] Kosar Univ Bojnord, Dept Math, POB 9415615458, Bojnord, Iran

关键词: Generalized Euler-Maclaurin summation formula;    Product integration rule;    Rate of convergence;    Singular integral;    Fermi-Dirac integral;   

DOI  :  10.1016/j.cam.2017.12.017

来源: Elsevier

【 摘 要 】

The present paper deals with a variant of the generalized Euler-Maclaurin summation formula for the product integration rule. The main idea lies on introducing a mesh associated with the integral of the square root of the weight function. We construct the set of nodes and implement it for approximating the considered integrals. It is shown theoretically that the proposed quadrature rule is of fourth order. The results of the provided numerical examples confirm the theoretical prediction. Moreover, applications of the suggested scheme for approximating some real test problems such as weakly singular integrals, including a particular case of the Fermi-Dirac integral, are investigated. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

Free