Article ID Journal Published Year Pages File Type
4637225 Applied Mathematics and Computation 2006 10 Pages PDF
Abstract

In this paper, we discuss about numerical improvement of the Open Newton–Cotes integration rules that are in forms of:∫a=x-1b=xn+1=x-1+(n+2)hf(x)dx≃∑k=0nBk(n)f(x-1+(k+1)h).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 the integral 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 the above integration formula up to degree n + 2. In this way, some numerical tests are given to show the numerical superiority of our idea with respect to the usual Open Newton–Cotes integration rules.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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