Summary
For the numerical evaluation of\(\int\limits_a^b {(t - a)^{\alpha - 1} x(t)dt}\), 0<α<1 andx ‘smooth’, product integration rules are applied. It is known that high-order rules, e.g. Gauss-Legendre quadrature, become ‘normal’-order rules in this case. In this paper it is shown that the high order is preserved by a nonequidistant spacing. Furthermore, the leading error terms of this product integration method and numerical examples are given.
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Schneider, C. Produktintegration mit nicht-äquidistanten Stützstellen. Numer. Math. 35, 35–43 (1980). https://doi.org/10.1007/BF01396368
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DOI: https://doi.org/10.1007/BF01396368