Quadrature rules for Prandtl's integral equation |
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Authors: | Prof G Monegato Dr V Pennacchietti |
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Affiliation: | 1. Dipartimento di Matematica, Politecnico di Torino, C. so Duca degli Abruzzi, 24, I-10128, Torino, Italy 2. Dipartimento di Matematica, Università di Catania, Italy
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Abstract: | In this paper we construct an interpolatory quadrature formula of the type $$\mathop {\rlap{--} \smallint }\limits_{ - 1}^1 \frac{{f'(x)}}{{y - x}}dx \approx \sum\limits_{i = 1}^n {w_{ni} (y)f(x_{ni} )} ,$$ wheref(x)=(1?x)α(1+x)β f o(x), α, β>0, and {x ni} are then zeros of then-th degree Chebyshev polynomial of the first kind,T n (x). We also give a convergence result and examine the behavior of the quantity \( \sum\limits_{i = 1}^n {|w_{ni} (y)|} \) asn→∞. |
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