Higher-order Newton-Cotes rules with end corrections

摘要

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.