Paper Info
Title
Improvement of the double exponential formula with conformal maps based on the locations of singularities
Abstract
The double exponential formula, or the DE formula, is a high-precision integration formula using a change of variables called a DE transformation. However, it has a disadvantage that it is sensitive to singularities of an integrand near the real axis, and Slevinsky and Olver (SIAM J. Sci. Comput., 2015) attempted to improve it by constructing conformal maps based on the locations of singularities. In this letter, we construct a new transformation formula based on their ideas. This can be regarded as a generalization of the DE transformations. We confirm the effectiveness of this by a numerical experiment.
Year
DOI
Venue
2019
10.14495/jsiaml.11.65
JSIAM LETTERS
Keywords
Field
DocType
numerical integration,double exponential formula,conformal maps
Mathematical analysis,Numerical integration,Conformal map,Gravitational singularity,Double exponential function,Mathematics
Journal
Volume
ISSN
Citations 
11
1883-0609
0
PageRank 
References 
Authors
0.34
0
2
Name
Order
Citations
PageRank
Shunki Kyoya100.34
kenichiro217433.20