Data for: Comparison of integration rules in the case of very narrow chromatographic peaks. Rules_Erf.xlsx
This spreadsheet demonstrates errors of partial integration of Gaussian peak using different rules. Peak section is digitized using 3,5,7,9,11 or 15 points. Integration is performed using Trapezoidal, Simpson's, and rules based on Euler-Maclaurin formula. Column with the name Euler-Maclaurin contains rule with properly calculated first derivative term. Columns Average rule 1, Average rule 2 and (Av.rule 1 + Av.rule2)/2 correspond to Euler-Maclaurin formula with 1st derivative calculated using finite differences as described in Theory section of the paper. True Euler-Maclaurin rule is always the best. Trapezoidal rule is preferable at very low data rates (less than 0.7 pts/sigma) and full area integration. Errors of Simpson's 1/3 and Average rule1, 2 and (Av.1+Av.2)/2 rules are comparable, as all of them account for the second derivative term of Taylor series and use finite differences.