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The evaluation of improper integrals encountered in the use of conformal transformation
Author(s) -
Binns K. J.,
Rees G. R.,
Kahan P.
Publication year - 1979
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620140408
Subject(s) - conformal map , gravitational singularity , mathematics , singularity , transformation (genetics) , simple (philosophy) , numerical integration , quadrature (astronomy) , mathematical analysis , gauss , limit (mathematics) , point (geometry) , gaussian quadrature , integral equation , nyström method , geometry , physics , biochemistry , chemistry , philosophy , epistemology , quantum mechanics , gene , optics
Methods are described and reviewed for the accurate numerical evaluation of improper integrals encountered in conformal transformation solutions involving boundaries of relatively complicated shape. Four methods are reviewed for the solution of integrals containing end‐point singularities. Two new methods are discussed for the solution of integrals containing both end point singularities and simple poles within the range of integration. One method uses a combination of a simple recursive formula and the coefficients of a Chebyshev series and a second method involves subtracting out the singularity and the use of Gauss–Jacobi quadrature. Both methods can give results of high accuracy and an upper limit of the error is readily found. A numerical example is taken which is typical of the application to practical problems and this brings out a comparison of the two methods.