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On bicubic transformation for the numerical evaluation of Cauchy principal value integrals

โœ Scribed by Chen, T. Charles

Publisher
John Wiley and Sons
Year
1993
Tongue
English
Weight
210 KB
Volume
9
Category
Article
ISSN
1069-8299

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โœฆ Synopsis

Recently a bicubic transformation was introduced to numerically compute the Cauchy principal value (CPV) integrals. Numerical results show that this new method converges faster than the conventional Gauss-Legendre quadrature rule when the integrand contains different types of singularity. Assume is the singular point of a CPV integral. The point ; i divides the interval [ -1,1] into two parts: [ -1, f ] and [ f , I] . The bicubic transformation maps the intervals [ -1, ij] and [ij, 11 to the interval [ -1 , 1 ] with

the following constraints: it maps the point ij -E to p., and ij + E top., where p. is the largest Gaussian point of an n-point Gauss-Legendre quadrature rule, and E is a user-supplied constant. The n-point Gauss-Legendre quadruture rule is then applied. In contrast to ordinary expectation, further numerical experiment shows that smaller E does not always produce better results. In this paper we are concerned with the selection of E to yield rapid convergence of numerical integration when the bicubic transformation method is applied.

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