ISSN:
1069-8299
Keywords:
Engineering
;
Engineering General
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
,
Technology
Notes:
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 η is the singular point of a CPV integral. The point η divides the interval [-1, 1] into two parts: [-1, η] and [η, 1]. The bicubic transformation maps the intervals [-1, η] and [η, 1] to the interval [-1, 1] with the following constraints: it maps the point η - ∊ to μn, and η + ∊ to -μn, where μn is the largest Gaussian point of an n-point Gauss-Legendre quadrature rule, and ∊ 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 ∊ does not always produce better results. In this paper we are concerned with the selection of ∊ to yield rapid convergence of numerical integration when the bicubic transformation method is applied.
Additional Material:
3 Tab.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/cnm.1640090404
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