Abstract
This paper discusses on numerical improvement of the Newton–Cotes integration rules, which are in forms of: ∫ a b = a + nh f ( x ) d x ≃ ∑ k = 0 n B k ( n ) f ( a + kh ) . It is known that the precision degree of above formula is n + 1 for even n’s and is n for odd n’s. However, if its bounds are considered as two additional variables (i.e. a and h in fact) we reach a nonlinear system that numerically improves the precision degree of above integration formula up to degree n + 2. In this way, some numerical examples are given to show the numerical superiority of our approach with respect to usual Newton–Cotes integration formulas.
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