Quadrature rules with (not too many) derivatives

Details Quadrature rules with (not too many) derivatives Quadrature rules with (not too many) derivatives

2011-09-01

arxiv.org/abs/1109.0326v1

Mathematics

Classical Analysis and ODEs

Scientific paper

Quadrature formulas for $\int_a^b f(x) dx$ where derivative terms need only
be evaluated at $a$ and $b$ in the composite rule are identified. Error bounds
are given when $f:[a,b]\to\mathbb{R}$ satisfies $f^{(n-1)}$ is absolutely
continuous so that $f^{(n)}\in L^p([a,b])$, and when $f^{(n-1)}$ is merely
continuous.

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