1. Simpson Symmetrized and Surpassed
   Daniel J. Velleman
   Mathematics Magazine, Vol. 77, No. 1, February 2004, pp. 31-45.
2. A development of Simpson's rule for the classroom.
   McDowell, Eric L.
   Int. J. Comput. Numer. Anal. Appl. 3 (2003), no. 1, 9--15, MathSciNet.  
3. Sharp error bounds for the trapezoidal rule and Simpson's rule.  
   Cruz-Uribe, D.; Neugebauer, C. J.
   JIPAM. J. Inequal. Pure Appl. Math.  3  (2002),  no. 4, Article 49, 22 pp. (electronic), MathSciNet.  
4. Simpson's Rule with Constant Weights  
   R. S. Pinkham  
   College Math Journal: Volume 32, Number 2, (2001), Pages: 91-93.   
5. The modified Simpson's rule for line integrals.
   Siyyam, Hani I.
   J. Indian Acad. Math. 23 (2001), no. 1, 99--107, MathSciNet.  
6. A version of Simpson's rule for multiple integrals
   Horwitz, A.
   Journal of Computational and Applied Mathematics, v 134, n 1-2, Sep 1, 2001, p 1-11, Compendex.
7. Error bounds for Simpson's quadrature through zero mean Gaussian with covariance
   Hong, B. I.; Choi, S. H.; Hahm, N.
   Communications- Korean Mathematical Society, 2001, vol. 16, no. 4, pp. 691-701, Ingenta.  
8. A note on error term of Simpson's 1/3rd rule  
   Das, R. N.; Pradhan, G.  
   Internat. J. Math. Ed. Sci. Tech. 31 (2000), no. 2, 269--271, MathSciNet.  
9. An A-stable extended Simpson rule for the numerical integration of ordinary differential equations  
   Bildik, N.; Bulut, H.  
   Hadronic J. Suppl. 14 (1999), no. 4, 449--457, MathSciNet.  
10. An inequality of Ostrowski type and its applications for Simpson's rule and special means  
    Fedotov, I.; Dragomir, S. S.
    Math. Inequal. Appl. 2 (1999), no. 4, 491--499, MathSciNet.  
11. Model conversion and redesign of a sampled-data uncertain system using Simpson's Rule
    Shieh, Leang-San (Univ of Houston); Dikkala, Udayini; Hwang, Chyi Source:
    Journal of the Chinese Institute of Electrical Engineering, Transactions of the Chinese Institute of Engineers, Series E/Chung KuoTien Chi Kung Chieng Hsueh K'an, v 6, n 3, Aug, 1999, p 179-194, Compendex.  
12. Dynamical control of computations using the trapezoidal and Simpson's rules   
    Chesneaux, J. M.; Jézéquel, F.
    SCAN-97 (Lyon). J.UCS 4 (1998), no. 1, 2--10, Math. Sci. Net.
13. On a generalization of a functional equation associated with Simpson's rule.
    Kannappan, Pl.; Riedel, T.; Sahoo, P. K.
    Rocznik Nauk.-Dydakt. Prace Mat. No. 15 (1998), 85--101, MathSciNet.  
14. Using Simpson's Rule to Approximate Sums of Infinite Series  
    Rick Kreminski  
    The College Mathematics Journal, Vol. 28, No. 5. (Nov., 1997), pp. 368-376, Jstor.  
15. 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.  
16. A modification of Simpson's 1/3 rule
    Das, R. N.; Pradhan, G.
    Internat. J. Math. Ed. Sci. Tech. 28 (1997), no. 6, 908--910, Math. Sci. Net.
17. On a functional equation associated with Simpson's rule.
    Kannappan, Pl.; Riedel, T.; Sahoo, P. K.
    Results Math. 31 (1997), no. 1-2, 115--126, MathSciNet.  
18. Cubic Splines from Simpson's Rule (in Classroom Capsules)  
    Nishan Krikorian; Mark Ramras  
    The College Mathematics Journal, Vol. 27, No. 2. (Mar., 1996), pp. 124-126, Jstor.  
19. A Note on Simpson's Rule  
    Ayoub B. Ayoub  
    Math. Comput. Ed. 30 (1996), no. 3, 292--294.  
20. The error estimate of an optimum numerical method of the compound Simpson rule for multidimensional integrals. (Chinese)
    Guo, Sen Lin
    Math. Practice Theory 26 (1996), no. 2, 84--89, MathSciNet.  
21. Formules optimales de quadrature attachées à la formule de quadrature du trapèze et à la formule de Simpson. (French) [Optimal quadrature formulas associated with the trapezoidal rule and the Simpson formula]
    Acu, Dumitru
    Studia Univ. Babes-Bolyai Math. 41 (1996), no. 2, 9--15, MathSciNet.  
22. Why Simpson's Rule is Exact for Cubics  
    David E. Dobbs and John C. Peterson  
    Math. Comput. Ed. 29 (1995), no. 1, 19--24.  
23. Numerical Methods for Improper Integrals  
    Gerald Flynn  
    The College Mathematics Journal, Vol. 26, No. 4. (Sep., 1995), pp. 284-291, Jstor.  
24. Evaluation of Cauchy principal-value integrals using modified Simpson rules
    Amari, S.
    Appl. Math. Lett. 7 (1994), no. 3, 19--23, MathSciNet.  
25. Novel IIR differentiator from the Simpson integration rule
    Al-Alaoui, Mohamad Adnan
    Transactions on Circuits and Systems I: Fundamental Theory and Applications, v 41, n 2, Feb, 1994, p 186-187, Compendex.
26. A Teachable Derivation of Asymptotic Error Expansions for Numerical Integration  
    Gal-Ezer, Judith  
    Mathematics and computer education, 1994, vol. 28, no. 3, pp. 303, Ingenta.  
27. Simpson's rule for numerical integration:.
    Chorlton, Frank
    Mathematical spectrum, 1994, vol. 27, no. 1, pp. 13, Ingenta.  
28. Probabilistic Analysis of Simpson's Quadrature.
    Choi, Sung Hee
    Journal of complexity, 1994, vol. 10, no. 4, pp. 384, Ingenta.  
29. A generalization of Simpson's rule  
    Horwitz, A.  
    Approx. Theory Appl. (N.S.) 9 (1993), no. 2, 71--80, Math. Sci. Net.
30. A Short Proof for Romberg Integration (in Notes)  
    T. von Petersdorff  
    American Mathematical Monthly, Vol. 100, No. 8. (Oct., 1993), pp. 783-785, Jstor. 
31. A nodal spline interpolant for the Gregory rule of even order
    J. M. DeVilliers
    Numer. Math., Vol. 66, 1993, pp. 123-137.  
32. A Pre-Calculus Method for Deriving Simpson's Rule  
    White, John  
    Pi mu epsilon journal, 1991, vol. 9, no. 4, pp. 214, Ingenta.  
33. Simpson's rule of discretized Feynman path integration.
    Zhang, Peisen
    J. Sci. Comput. 6 (1991), no. 1, 47--60, MathSciNet.  
34. On a generalization of compound Newton-Cotes quadrature formulas
    Peter Kohler
    BIT, Vol. 31, 1991, pp. 540-544.
35. The use of the Euler functions for error estimates of the trapezoidal and Simpson's quadratures  
    Yue-Kuen Kwok  
    Int. J. Math. Educ. Sci. Technol.,Vol. 21, No. 6, (1990), pp. 863-870.  
36. An improved rule for qadrature that is closer to the trapezium rule than Simpson's rule  
    N. J. Royce  
    Int. J. Math. Educ. Sci. Technol.,Vol. 21, No. 4, (1990), pp. 551-558.    
37. Teaching Numerical Integration in a Revitalized Calculus  
    Temple H. Fay  
    Math. Comput. Ed. 24 (1990), no. 3, 240--247.
38. A Clamped Simpson's Rule  
    James A. Uetrecht  
    The College Mathematics Journal, Vol. 19, No. 1. (Jan., 1988), pp. 43-52, Jstor.  
39. Applications of Transformations to Numerical Integration  
    Chris W. Avery and Frank P. Soler  
    College Math Journal: Volume 19, Number 2, Pages: 166-167, 1988.  
40. Archimedes' Quadrature and Simpson's Rule (in Classroom Capsules)  
    Frank Burk  
    The College Mathematics Journal, Vol. 18, No. 3. (May, 1987), pp. 222-223, Jstor.  
41. Romberg Integration by Taylor Series (in Notes)  
    Edward R. Rozema  
    American Mathematical Monthly, Vol. 94, No. 3. (Mar., 1987), pp. 284-288, Jstor.  
42. Perfect Numerical Integration and Odd Functions  
    H. V. Smith  
    The Mathematical Gazette, Vol. 70, no. 452, (June, 1986), pp. 143-144.  
43. Numerical Integration via Integration by Parts (in Classroom Capsules)  
    Frank Burk  
    The College Mathematics Journal, Vol. 17, No. 5. (Nov., 1986), pp. 418-422, Jstor.  
44. An adaptive Simpson quadrature algorithm for learning purposes  
    D. Katsifli  and  D. J. Fyfe  
    Int. J. Math. Educ. Sci. Technol.,Vol. 14, No. 3, (1983), pp. 341-350.  
45. A method for finding error terms (quadrature)  
    A. McD.Mercer  
    Int. J. Math. Educ. Sci. Technol.,Vol. 14, No. 5, pp. 579-582, 1983.   
46. Errors in Simpson's composite quadrature formulas, and the "three-eighths rule". (Russian)
    Kuzyutin, V. F.
    Mathematical methods of optimization and control in complex systems, 154--157, Kalinin. Gos. Univ., Kalinin, 1983., MathSciNet.  
47. A method of using Simpson's rule in the DFT
    Roddy, D.
    IEEE Trans. Acoust. Speech Signal Process. 29 (1981), no. 4, 936--937, MathSciNet.  
48. Approximate Integration: Comparative Examples  
    Stewart M. Venit  
    The Mathematics Teacher, Vol. 71, No. 9, pp. 774-775, December, 1978.  
49. A Short Program for Simpson's or Gazdar's Rule-Integration on Handheld Programmable Calculators (in Computer Corner)  
    Abdus Sattar Gazdar  
    The Two-Year College Mathematics Journal,Vol.9, No.3. (Jun.,1978),pp.182-185, Jstor.  
50. 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.  
51. Numerical Integration by Polynomial Interpolation  
    Jackie L. Lawrence  
    Pi Mu Epsilon Journal, Vol. 6, No. 6, pp. 337-344, 1977.   
52. On the discretisation error of the weighted Simpson rule  
    Wang, Jesse Y. Nordisk Tidskr.
    Informationbehandling (BIT) 16 (1976), no. 2, 205--214, MathSciNet.  
53. Perfect Numerical Integration by Simpson's Rule  
    R. F. Churchhouse  
    The Mathematical Gazette, Vol. 59, no. 409, pp. 159-162, Oct., 1975, Math. Sci. Net.  
54. Errors in Simpson's complex quadrature formulas and the rule of "three eights" on some classes of functions. (Russian)
    Kuzjutin, V. F.
    Metody i Modeli Upravlenija Vyp. 9 (1975), 92--94, 210--211, MathSciNet.  
55. 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.   
56. Exit Criteria for Simpson's Compound Rule  
    J. H. Rowland, Y. L. Varol  
    Mathematics of Computation, Vol. 26, No. 119. (Jul., 1972), pp. 699-703, Jstor.  
57. Generalized Simpson's rule  
    Bergström, Arne  
    Nordisk Mat. Tidskr. 20 (1972), 138--142, 159, Math. Sci. Net.
58. Monotonicity in Romberg Quadrature  
    Torsten Strom  
    Mathematics of Computation, Vol. 26, No. 118. (Apr., 1972), pp. 461-465, Jstor.  
59. 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.  
60. On generalised Simpson's rule with end corrections   
    Sen, Syamal Kumar  
    J. Indian Inst. Sci. 52 (1970) 63--68, Math. Sci. Net.
61. 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.  
62. 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.  
63. Note on Simpson's Rule (in Classroom Notes)  
    Anon  
    American Mathematical Monthly, Vol. 76, No. 8. (Oct., 1969), pp. 929-930, Jstor.  
64. Notes on the adaptive Simpson quadrature routine.  
    Lyness, J. N.  
    J. Assoc. Comput. Mach. 16 1969 483--495, MathSciNet.  
65. Neville's and Romberg's Processes: A Fresh Appraisal with Extensions  
    J. C. P. Miller  
    Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 263, No. 1144. (Dec. 24, 1968), pp. 525-562, Jstor.  
66. On the Method of Romberg Quadrature  
    A. Meir, A. Sharma  
    Journal of the Society for Industrial and Applied Mathematics: Series B, Numerical Analysis, Vol. 2, No. 2. (1965), pp. 250-258, Jstor.  
67. Error Estimates for Romberg Quadrature  
    A. H. Stroud  
    Journal of the Society for Industrial and Applied Mathematics: Series B, Numerical Analysis, Vol. 2, No. 3. (1965), pp. 480-488 , Jstor.  
68. Simpson's Rule for Unequally Spaced Ordinates (in Classroom Notes)  
    N. Shklov
    American Mathematical Monthly, Vol. 67, No. 10. (Dec., 1960), pp. 1022-1023, Jstor.  
69. Newton-Cotes Quadrature Formulas (in Classroom Notes)  
    D. S. Greenstein  
    The American Mathematical Monthly, Vol. 62, No. 7. (Aug. - Sep., 1955), pp. 487-488, Jstor.  
70. 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.  
71. A "Simpson's rule" for the numerical evaluation of Wiener's integrals in function space.
    Cameron, R. H.
    Duke Math. J. 18, (1951). 111--130, MathSciNet.  
72. 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.  
73. 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.  
74. Discussions: On the Relative Accuracy of Simpson's Rules and Weddle's Rule A Reply (in Questions and Discussions)  
    J. B. Scarborough  
    American Mathematical Monthly, Vol. 34, No. 7. (Aug. - Sep., 1927), pp. 370-372, Jstor.  
75. Discussions: On the Relative Accuracy of Simpson's Rules and Weddle's Rule A Question (in Questions and Discussions)  
    Raymond Garver  
    American Mathematical Monthly, Vol. 34, No. 7. (Aug. - Sep., 1927), p. 369, Jstor.  
76. Discussions: On the Relative Accuracy of Simpson's Rules and Weddle's Rule (in Questions and Discussions)  
    J. B. Scarborough  
    American Mathematical Monthly, Vol. 34, No. 3. (Mar., 1927), pp. 135-139, Jstor.  
77. Formulas for the Error in Simpson's Rule  
    J. B. Scarborough  
    American Mathematical Monthly, Vol. 33, No. 2. (Feb., 1926), pp. 76-83, Jstor.  

(c) John H. Mathews 2004