A corrected quadrature formula and applications

A straightforward 3-point quadrature formula of closed type is derived that improves on Simpson's rule. Just using the additional information of the integrand's derivative at the two endpoints we show the error is sixth order in grid spacing. Various error bounds for the quadrature formula are obtained to quantify more precisely the errors. Applications in numerical integration are given. With these error bounds, which are generally better than the usual Peano bounds, the composite formulas can be applied to integrands with lower order derivatives

A corrected quadrature formula and applications

A straightforward three-point quadrature formula of closed type is derived that improves on Simpson's rule. Just using the additional information of the integrand's derivative at the two endpoints we show the error is sixth order in grid spacing. Various error bounds for the quadrature formula are obtained to quantify more precisely the errors. Applications in numerical integration are given. With these error bounds, which are generally better than the usual Peano bounds, the composite formulas can be applied to integrands with lower order derivatives

A generalization of the modified Simpson's rule and error bounds

A generalization of the modified Simpson's rule is derived. Various error bounds for this generalization are established. An application to Dawson integral is given. References G. A. Anastassiou, Ostrowski type inequalities, Proc. Amer. Math. Soc., Vol. 123(12), (1995), 3775--3781. P. Cerone and S. S. Dragomir, Midpoint-type rules from an inequalities point of view, handbook of analytic-computational methods in applied mathematics, Editor: G. Anastassiou, CRC Press, New York, (2000), 135--200. P. Cerone and S. S. Dragomir, Trapezoidal-type rules from an inequalities point of view, handbook of analytic-computational methods in applied mathematics, Editor: G. Anastassiou, CRC Press, New York, (2000), 65--134. Lj. Dedic, M. Matic and J. Pecaric, On Euler trapezoid formulae, Appl. Math. Comput., 123 (2001), 37--62. http://dx.doi.org/10.1016/S0096-3003(00)00054-0 C. E. M. Pearce, J. Pecaric, N. Ujevic and S. Varosanec, Generalizations of some inequalities of Ostrowski--Gruss type, Math. Inequal. Appl., 3(1), (2000), 25--34. http://www.mia-journal.com/files/3-1/full/03-03.PDF N. Ujevic and A. J. Roberts, A corrected quadrature formula and applications, ANZIAM J., 45(E), (2004), E41--E56. http://anziamj.austms.org.au/V45/E05

On Generalized Taylor's Formula and Some Related Results

[[abstract]]The classical and generalized Taylor's formula are considered. Some improvements of earlier derived results are obtained

Generalizations of some inequalities of Ostrowski-Gruss type

Charles E. M. Pearce, Josip Pečarić, Nenad Ujević, Sanja Varošane