Abstract
We present higher-order quadrature rules with end corrections for general Newton–Cotes quadrature rules. The construction is based on the Euler–Maclaurin formula for the trapezoidal rule. We present examples with 6 well-known Newton–Cotes quadrature rules. We analyze modified end corrected quadrature rules, which consist on a simple modification of the Newton–Cotes quadratures with end corrections. Numerical tests and stability estimates show the superiority of the corrected rules based on the trapezoidal and the midpoint rules.
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