Bibliography

for

Simpson's Rule for Numerical Integration

Return to Numerical Methods - Numerical Analysis

 

 

  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, MathSciNet.    
  5. 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.  
  6. 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.  
  7. Using Simpson's rule to approximate sums of infinite series  
    Kreminski, Rick  
    College Math. J. 28 (1997), no. 5, 368--376, MathSciNet.  
  8. Understanding the Extra Power of the Newton-Cotes Formula  
    Kenneth J. Supowit  
    Mathematics Magazine: Volume 70, Number 4, (1997), Pages: 292-293.   
  9. 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.
  10. Cubic Splines from Simpson's Rule  
    Nishan Krikorian and Mark Ramras  
    College Math Journal: Volume 27, Number 2, (1996), Pages: 124-126.  
  11. A Note on Simpson's Rule  
    Ayoub B. Ayoub  
    Math. Comput. Ed. 30 (1996), no. 3, 292--294.  
  12. Why Simpson's Rule is Exact for Cubics  
    David E. Dobbs and John C. Peterson  
    Math. Comput. Ed. 29 (1995), no. 1, 19--24.  
  13. Numerical Methods for Improper Integrals  
    Gerald Flynn  
    College Math Journal: Volume 26, Number 4, Pages: 284-291, 1995
  14. 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.  
  15. A Short Proof for Romberg Integration (in Notes)  
    T. von Petersdorff  
    American Mathematical Monthly, Vol. 100, No. 8. (Oct., 1993), pp. 783-785, Jstor.  
  16. A Pre-Calculus Method for Deriving Simpson's Rule  
    White, John  
    Pi mu epsilon journal, 1991, vol. 9, no. 4, pp. 214, Ingenta.  
  17. On a generalization of compound Newton-Cotes quadrature formulas
    Peter Kohler
    BIT, Vol. 31, 1991, pp. 540-544.
  18. 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.  
  19. 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.    
  20. Teaching Numerical Integration in a Revitalized Calculus  
    Temple H. Fay  
    Math. Comput. Ed. 24 (1990), no. 3, 240--247.
  21. A Clamped Simpson's Rule  
    James A. Uetrecht  
    College Math Journal: Volume 19, Number 1, (1988), Pages: 43-52.  
  22. Applications of Transformations to Numerical Integration  
    Chris W. Avery and Frank P. Soler  
    College Math Journal: Volume 19, Number 2, Pages: 166-167, 1988.  
  23. Archimedes' Quadrature and Simpson's Rule  
    Frank Burk  
    College Math Journal: Volume 18, Number 3, (1987), Pages: 222-223.  
  24. Romberg Integration by Taylor Series (in Notes)  
    Edward R. Rozema  
    American Mathematical Monthly, Vol. 94, No. 3. (Mar., 1987), pp. 284-288, Jstor.  
  25. Perfect Numerical Integration and Odd Functions  
    H. V. Smith  
    The Mathematical Gazette, Vol. 70, no. 452, (June, 1986), pp. 143-144.  
  26. Numerical Integration via Integration by Parts  
    Frank Burk  
    College Math Journal: Volume 17, Number 5, Pages: 418-422, 1986.
  27. 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.  
  28. A method for finding error terms (quadrature)  
    A. McD.Mercer  
    Int. J. Math. Educ. Sci. Technol.,Vol. 14, No. 5, pp. 579-582, 1983.   
  29. Approximate Integration: Comparative Examples  
    Stewart M. Venit  
    The Mathematics Teacher, Vol. 71, No. 9, pp. 774-775, December, 1978.  
  30. 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.  
  31. Numerical Integration by Polynomial Interpolation  
    Jackie L. Lawrence  
    Pi Mu Epsilon Journal, Vol. 6, No. 6, pp. 337-344, 1977.   
  32. 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.  
  33. 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.   
  34. 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.  
  35. Monotonicity in Romberg Quadrature  
    Torsten Strom  
    Mathematics of Computation, Vol. 26, No. 118. (Apr., 1972), pp. 461-465, Jstor.  
  36. 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.  
  37. 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.  
  38. 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.  
  39. Note on Simpson's Rule (in Classroom Notes)  
    Anon  
    American Mathematical Monthly, Vol. 76, No. 8. (Oct., 1969), pp. 929-930, Jstor.  
  40. 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.  
  41. 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.  
  42. 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.  
  43. 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.  
  44. 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.  
  45. 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.  
  46. 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.  
  47. 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.  
  48. 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.  
  49. 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.  
  50. 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