TY  - JOUR
ID  - epprod3780
UR  - http://dx.doi.org/10.1016/j.cam.2006.03.012
IS  - 1
A1  - Elliott, D
A1  - Johnston, PR
Y1  - 2007///
N2  - In the two-dimensional boundary element method, one often needs to evaluate numerically integrals of the form  where j2 is a quadratic, g is a polynomial and f is a rational, logarithmic or algebraic function with a singularity at zero. The constants a and b are such that -1a1 and 0<b1 so that the singularities of f will be close to the interval of integration. In this case the direct application of Gauss?Legendre quadrature can give large truncation errors. By making the transformation x=a+bsinh(?u-?), where the constants ? and ? are chosen so that the interval of integration is again [-1,1], it is found that the truncation errors arising, when the same Gauss?Legendre quadrature is applied to the transformed integral, are much reduced. The asymptotic error analysis for Gauss?Legendre quadrature, as given by Donaldson and Elliott [A unified approach to quadrature rules with asymptotic estimates of their remainders, SIAM J. Numer. Anal. 9 (1972) 573?602], is then used to explain this phenomenon and justify the transformation.
PB  - Elsevier Science BV
JF  - Journal of Computational and Applied Mathematics
VL  - 203
KW  - Numerical integration; Boundary element method; Nearly singular integrals; Nonlinear coordinate transformation; Sinh function
SN  - 0377-0427
TI  - Error analysis for a sinh transformation used in evaluating nearly singular boundary element integrals
SP  - 103
AV  - restricted
EP  - 124
ER  -