Bibliography for Newton-Cotes Integration

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  1. A unified approach to Newton-Cotes quadrature formulae
    El-Mikkawy, Moawwad
    Applied Mathematics and Computation (New York), v 138, n 2-3, Jun 20, 2003, p 403-413, Compendex.
  2. A Newton-Cotes quadrature approach for solving the aerosol coagulation equation
    Sandu, A.
    Atmospheric Environment, v 36, n 3, 2002, p 583-589, Compendex.
  3. Understanding the Extra Power of the Newton-Cotes Formula for Even Degree (in Notes)  
    Kenneth J. Supowit  
    Mathematics Magazine, Vol. 70, No. 4. (Oct., 1997), pp. 292-293, Jstor.  
  4. On the error and its control in a two-parameter generalised Newton-Cotes rule.   
    Ehrenmark, Ulf Torsten   
    J. Comput. Appl. Math. 75 (1996), no. 1, 171--195, MathSciNet.  
  5. Programmable incoherent Newton-Cotes optical integrator
    Ngo, Nam Q.; Binh, Le Nguyen
    Optics Communications, v 119, n 3-4, Sep 1, 1995, p 390-402, Compendex.
  6. On Gregory- and Modified Gregory-type Corrections to Newton-Cotes Quadrature.
    Bocher, P.; De Meyer, H.; Vanden Berghe, G.
    Journal of computational and applied mathematics, 1994, vol. 50, no. 1/3, pp. 145-158, Ingenta.
  7. Numerical Evaluation of Line Integrals  
    K. Atkinson; E. Venturino  
    SIAM Journal on Numerical Analysis, Vol. 30, No. 3. (Jun., 1993), pp. 882-888, Jstor.  
  8. Generating functions for Newton-Cotes formulae weights and error terms.   
    Brock, Bradley W.   
    Appl. Anal. 47 (1992), no. 2-3, 103--106, MathSciNet.  
  9. A note on the Newton-Cotes integration formula.  
    Mills, T. M.; Smith, Simon J.  
    J. Approx. Theory 66 (1991), no. 1, 98--105, MathSciNet.  
  10. Estimating Integrals Using Quadrature Methods with an Application in Pharmacokinetics (in The Consultant's Forum)  
    A. John Bailer; Walter W. Piegorsch  
    Biometrics, Vol. 46, No. 4. (Dec., 1990), pp. 1201-1211, Jstor.  
  11. Newton-Cotes rules for triple integrals
    Sadiku, M. N. O; Kiem, Raymond Jong A.  
    Conference Proceedings - IEEE SOUTHEASTCON, v 2, 1990, p 471-475, Compendex.
  12. The Generating Function Method of Nonlinear Approximation  
    R. D. Small  
    SIAM Journal on Numerical Analysis, Vol. 25, No. 1. (Feb., 1988), pp. 235-244, Jstor.  
  13. Improvements Of Adaptive Newton-Cotes Quadrature Methods.
    Ninomiya, Ichizo
    Journal of Information Processing, v 3, n 3, 1980, p 162-170, Compendex.
  14. On average Newton-Cotes quadrature formulas.   
    Omladic, M.  
    J. Inst. Math. Appl. 21 (1978), no. 4, 493--498, MathSciNet.  
  15. Exit Criteria for Newton-Cotes Quadrature Rules  
    J. H. Rowland, G. J. Miel  
    SIAM Journal on Numerical Analysis, Vol. 14, No. 6. (Dec., 1977), pp. 1145-1150, Jstor.  
  16. Generating and compounding product-type Newton-Cotes quadrature formulas.  
    Duris, Charles S.  
    ACM Transactions on Mathematical Software, v 2, n 1, Mar, 1976, p 50-58, Compendex.
  17. Some Comments on the Derivation and Structure of Newton-Cotes Quadrature Formulae  
    Ayse Alaylioglu,  G. A. Evans  and  J. Hyslop  
    Int. J. Math. Educ. Sci. Technol.,Vol. 5, (1974), pp. 213-217.   
  18. Monotonicity of Quadrature Approximations  
    D. J. Newman  
    Proceedings of the American Mathematical Society, Vol. 42, No. 1. (Jan., 1974), pp. 251-257, Jstor.  
  19. Norm Bounds of Quadrature Processes  
    Franz Locher  
    SIAM Journal on Numerical Analysis, Vol. 10, No. 4. (Sep., 1973), pp. 553-558, Jstor.  
  20. Estimates of Upper Bounds for Quadrature Errors  
    J. D. Donaldson  
    SIAM Journal on Numerical Analysis, Vol. 10, No. 1. (Mar., 1973), pp. 13-22, Jstor.  
  21. Contribution to the numerical solution of differential equations by means of Runge-Kutta formulas with Newton-Cotes numbers weights.  
    Hut'a, Anton  
    Acta Fac. Rerum Natur. Univ. Comenian. Math. Publ. 28 (1972), 51--65, MathSciNet.  
  22. Addendum to "A Proof of the Newton-Cotes Quadrature Formulas with Error Term"  
    D. R. Hayes, L. Rubin  
    American Mathematical Monthly, Vol. 78, No. 9. (Nov., 1971), p. 988, Jstor.  
  23. A Proof of the Newton-Cotes Quadrature Formulas with Error Term  
    D. R. Hayes, L. Rubin  
    American Mathematical Monthly, Vol. 77, No. 10. (Dec., 1970), pp. 1065-1072, Jstor.  
  24. Error of the Newton-Cotes and Gauss-Legendre Quadrature Formulas  
    N. S. Kambo  
    Mathematics of Computation, Vol. 24, No. 110. (Apr., 1970), pp. 261-269, Jstor.  
  25. Newton-Cotes formulae in n-dimensions.  
    Guenther, R. B.; Roetman, E. L.  
    Numer. Math. 14 1969/1970 330--345, MathSciNet.  
  26. Newton-Cotes type quadrature formulas with terminal corrections.  
    Sack,R.A.  
    Comput.J.5 1962/1963 230--237, MathSciNet.  
  27. Newton-Cotes Quadrature Formulas (in Classroom Notes)  
    D. S. Greenstein  
    American Mathematical Monthly, Vol. 62, No. 7. (Aug. - Sep., 1955), pp. 487-488, Jstor.  
  28. A Note on Newton-Cotes Quadrature Formulas (in Classroom Notes)  
    Morris Morduchow  
    American Mathematical Monthly, Vol. 62, No. 1. (Jan., 1955), pp. 33-35, Jstor.  
  29. Approximate Product-Integration  
    Andrew Young  
    Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 224, No. 1159. (Jul. 22, 1954), pp. 552-561, Jstor.  
  30. On the Expansion of the Remainder in the Open-Type Newton-Cotes Quadrature Formula  
    Orville G. Harrold, Jr.  
    American Journal of Mathematics, Vol. 59, No. 2. (Apr., 1937), pp. 275-289, Jstor.  
  31. On the Expansion of the Remainder in the Newton-Cotes Formula  
    J. V. Uspensky  
    Transactions of the American Mathematical Society, Vol. 37, No. 3. (May, 1935), pp. 381-396, Jstor.  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004