ISSN:
1572-9125
Keywords:
Cauchy principal value
;
spline
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract In this paper, quasi-interpolating splines are used to approximate the Cauchy principal value integral $$J(w_{\alpha \beta } f;\lambda ): = \smallint - _{ - 1}^1 w_{\alpha \beta } (x)\frac{{f(x)}}{{x - \lambda }}dx, \lambda \in ( - 1,1)$$ where $$w_{\alpha \beta } (x): = (1 - x)^\alpha (1 + x)^\beta ,\alpha ,\beta 〉 - 1.$$ . We prove uniform convergence for the quadrature rules proposed here and give an algorithm for the numerical evaluation of these rules.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01737167
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