Quadrature rules using an arbitrary fixed order of derivatives

Authors:
M. R. Eslahchi;Mehdi Dehghan
Affiliations:
Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No 424, Hafez Ave, Tehran, Iran;Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No 424, Hafez Ave, Tehran, Iran
Venue:
Computers & Mathematics with Applications
Year:
2009

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Abstract

In this paper we consider quadrature formulas which use the derivative of only an arbitrary fixed order (m) of function f at the nodes. One of the advantages of the new approach is that we can increase the precision degree of the n-point quadrature formulas from 2n-1 to 2n+m-1. Furthermore we give an asymptotic estimation for the rate of convergence of this formula. Some examples will be given to support the results.