1. An Optimum Generalized Trapezoidal Formula for the Numerical Integration of y' = f(x,y)  
   Jain, M. K.  
   International Journal of Computer Mathematics, 2001, vol. 77, no. 2, pp. 333-334, Ingenta.   
2. Bounds of zero mean Gaussian with covariance for average error of trapezoidal rule
   Hong, B. I.; Choi, S. H.; Hahm, N.
   Korean Journal of Computational and Applied Mathematics Series A, 2001, vol. 8, no. 1,
   pp. 231-242, Ingenta.   
3. The "Modified Trapezoidal Rule" (theta-Method) for the Integration of DAEs Modelling an Electro-Mechanical Drive Including External Circuitry and Magnetic Field-Distribution
   Klocke, M.
   Lecture Notes in Computational Science and Engineering, 2001, vol. 18, pp. 397-406, Ingenta.   
4. Some Error Estimates in the Trapezoidal Quadrature Rule
   Dragomir, S. S.; Mabizela, S.
   Tamsui Oxford Journal of Mathematical Sciences, 2000, vol. 16, no. 2, pp. 259-272, Ingenta.   
5. A multi-time step integration algorithm for structural dynamics based on the modified trapezoidal rule.
   Wu, Y.S.; Smolinski, P.
   Computer Methods in Applied Mechanics and Engineering, 2000, vol. 187, no. 3/4, pp. 641, Ingenta.   
6. Hybrid Gauss-Trapezoidal Quadrature Rules.
   Alpert, Bradley K.
   SIAM journal on scientific computing, 1999, vol. 20, no. 5, pp. 1551, Ingenta.   
7. Sigmoidal transformations and the trapezoidal rule  
   Elliott, David  
   J. Austral. Math. Soc. Ser. B 40 (1998/99), (E), E77--E137 (electronic), MathSciNet.  
8. 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 (electronic), MathSciNet.  
9. A fourth order extrapolation for the trapezoidal rule  
   Marfurt, M.; Urbani, A. M.  
   Calcolo 35 (1998), no. 2, 117--124, MathSciNet.  
10. On an error of trapezoidal rule  
    Hong, Bum Il; Choi, Sung Hee; Hahm, Nahmwoo  
    Commun. Korean Math. Soc. 13 (1998), no. 4, 903--911, MathSciNet.  
11. Asymptotic expansions for trapezoidal type product integration rules.
    Santos-Leon, J.C.
    Journal of computational and applied mathematics, 1998, vol. 91, no. 2, pp. 219, Ingenta.   
12. Subcycling First- and Second-order Generalizations of the Trapezoidal Rule.
    Daniel, W.J.T.
    International journal for numerical methods in e, 1998, vol. 42, no. 6, pp. 1091, Ingenta.   
13. Trapezoidal rule for multiple integrals over hyperquadrilaterals  
    Yeh, Tyan  
    Appl. Math. Comput. 87 (1997), no. 2-3, 227--246, MathSciNet.  
14. From the trapezoidal rule to higher-order accurate and unconditionally stable time-integration method for structural dynamics.
    Kim, Seung Jo; Cho, Jin Yeon; Kim, Wie Dae
    Symposium on Advances in Computational Mechanics, Vol. 1 (Austin, TX, 1997), MathSciNet.
15. The modified trapezoidal rule for line integrals  
    Siyyam, H. I.; Syam, M. I.  
    J. Comput. Appl. Math. 84 (1997), no. 1, 1--14, MathSciNet.  
16. High-Order Corrected Trapezoidal Quadrature Rules for Singular Functions.
    Kapur, Sharad; Rokhlin, Vladimir
    Siam journal on numerical analysis, 1997, vol. 34, no. 4, pp. 1331, Ingenta.   
17. On the potentiality of sequential and parallel codes based on extended trapezoidal rules (ETRs).
    Brugnano, L.; Trigiante, D.
    Applied numerical mathematics, 1997, vol. 25, no. 2/3, pp. 169, Ingenta.   
18. On the potentiality of sequential and parallel codes based on extended trapezoidal rules (ETRs)  
    Brugnano, Luigi; Trigiante, Donato  
    Special issue on time integration (Amsterdam, 1996). Appl. Numer. Math. 25 (1997), no. 2-3, 169--184, MathSciNet.  
19. Proof without Words: The Trapezoidal Rule (for Functions)  
    Urias, Jesus
    Mathematics magazine, 1995, vol. 68, no. 3, pp. 192, Ingenta.   
20. 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.   
21. Multivariate Boolean trapezoidal rules  
    Baszenski, Günter; Delvos, Franz-Jürgen  
    Approximation, probability, and related fields (Santa Barbara, CA, 1993), 109--117, Plenum, New York,1994, MathSciNet.  
22. Trapezoidal Stratified Monte Carlo Integration  
    Stamatis Cambanis, Elias Masry  
    SIAM Journal on Numerical Analysis, Vol. 29, No. 1. (Feb., 1992), pp. 284-301, Jstor.  
23. The high-order use of the trapezoidal rule in numerical quadrature  
    Evans, G. A.  
    Internat. J. Math. Ed. Sci. Tech. 23 (1992), no. 4, 525--536, MathSciNet.  
24. The relationship between the generalised mid-point and trapezoidal rules in incremental elasto-plasticity.
    Rencontre, L.J.; Caddemi, S.; Martin, J.B.
    Computer methods in applied mechanics and engineering, 1992, vol. 96, no. 2, pp. 201, Ingenta.   
25. Applications of the trapezoidal rule  
    Smith, H. V.
    J. Inst. Math. Comput. Sci. Math. Ser. 4 (1991), no. 3, 397--400, MathSciNet.  
26. Trapezoidal Monte Carlo Integration  
    Elias Masry, Stamatis Cambanis  
    SIAM Journal on Numerical Analysis, Vol. 27, No. 1. (Feb., 1990), pp. 225-246, Jstor.  
27. 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.   
28. 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.    
29. On some problems concerning best constants for the midpoint and trapezoidal rule  
    Büttgenbach, Bernhard; Lüttgens, Gerald; Nessel, Rolf J.
    General inequalities, 6 (Oberwolfach, 1990), 393--409, Internat. Ser. Numer. Math., 103, Birkhäuser, Basel, 1992, MathSciNet.  
30. Characterization of the speed of convergence of the trapezoidal rule  
    Rahman, Qazi I.; Schmeisser, Gerhard  
    Numer. Math. 57 (1990), no. 2, 123--138, MathSciNet.  
31. End-point corrected trapezoidal quadrature-diffusion singular functions.
    Rokhlin, V.
    Computers & mathematics with applications, 1990, vol. 20, no. 7, pp. 51, Ingenta.   
32. Asymptotic error expansions for stiff equations: an analysis for the implicit midpoint and trapezoidal rules in the strongly stiff case.
    Auzinger, W.; Frank, R.  
    Numer. Math. 56 (1989), no. 5, 469--499, MathSciNet.  
33. The trapezoidal rule for analytic functions of rapid decrease.
    Eggert, N.; Lund, J.
    Journal of computational and applied mathematics, 1989, vol. 27, no. 3, pp. 389, Ingenta.   
34. A fourth-order A-stable acceleration of the trapezoidal rule. (Italian)  
    Urbani, A. M. A  
    Calcolo 24 (1987), no. 3-4, 255--262 (1988), MathSciNet.  
35. Stability of trapezoidal rule methods with local extrapolation. (Chinese)  
    Tang, Ming Duan
    Math. Numer. Sinica 9 (1987), no. 3, 297--302, MathSciNet.  
36. A class of functions for which the trapezoidal rule gives the exact value of integral over the infinite interval.
    Sugihara, Masaaki  
    Proceedings of the 2nd international conference on computational and applied mathematics (Leuven, 1986). J. Comput. Appl. Math. 20 (1987), Special Issue, 387--392, MathSciNet.  
37. La règle optimale du trapèze pour l'intégrale de Riemann-Stieltjes d'une fonction donnée. (French)  
    [The optimal trapezoidal rule for the Riemann-Stieltjes integral of a given function]  
    Dubuc, Serge; Todor, Fabian  
    C. R. Math. Rep. Acad. Sci. Canada 9 (1987), no. 5, 213--218, MathSciNet.  
38. Behold! The Midpoint Rule is Better Than the Trapezoidal Rule for Concave Functions  
    Frank Buck  
    College Math Journal: Volume 16, Number 1, (1985), Pages: 56.   
39. Estimating the Error in the Trapezoidal Rule (in Classroom Notes)  
    Edward Rozema  
    American Mathematical Monthly, Vol. 87, No. 2. (Feb., 1980), pp. 124-128, Jstor.  
40. On Simplex Trapezoidal Rule Families  
    J. N. Lyness, A. C. Genz  
    SIAM Journal on Numerical Analysis, Vol. 17, No. 1. (Feb., 1980), pp. 126-147, Jstor.  
41. On Error Norms of the Trapezoidal Rule  
    Rainer Kress  
    SIAM Journal on Numerical Analysis, Vol. 15, No. 3. (Jun., 1978), pp. 433-443, Jstor.  
42. The Error of the Trapezoidal Method for a Concave Curve (in Classroom Notes)  
    S. K. Stein  
    American Mathematical Monthly, Vol. 83, No. 8. (Oct., 1976), pp. 643-645, Jstor.  
43. The Numerical Solution of an Abel Integral Equation by a Product Trapezoidal Method  
    Kendall E. Atkinson  
    SIAM Journal on Numerical Analysis, Vol. 11, No. 1. (Mar., 1974), pp. 97-101, Jstor.  
44. Some Minimum Properties of the Trapezoidal Rule  
    J. E. Dennis, Jr., Roland A. Sweet  
    SIAM Journal on Numerical Analysis, Vol. 9, No. 2. (Jun., 1972), pp. 230-236, Jstor.  
45. A Note on Trapezoidal Methods for the Solution of Initial Value Problems  
    A. R. Gourlay  
    Mathematics of Computation, Vol. 24, No. 111. (Jul., 1970), pp. 629-633, Jstor.  
46. A Simple "Filon-Trapezoidal" Rule (in Technical Notes and Short Papers)  
    E. O. Tuck  
    Mathematics of Computation, Vol. 21, No. 98. (Apr., 1967), pp. 239-241, Jstor.  
47. Further Examples of Exact Integration using the Trapezoidal Rule (in Mathematical Notes)  
    R. Butler  
    American Mathematical Monthly, Vol. 69, No. 6. (Jun. - Jul., 1962), pp. 534-538, Jstor.  
48. An Adjusted Trapezoidal Rule Using Function Values Within the Range of Integration (in Classroom Notes)  
    J. M. Wolfe  
    American Mathematical Monthly, Vol. 66, No. 2. (Feb., 1959), pp. 125-127, Jstor.  
49. Trapezoidal Methods of Approximating Solutions of Differential Equations  
    Preston C. Hammer, Jack W. Hollingsworth  
    Mathematical Tables and Other Aids to Computation, Vol. 9, No. 51. (Jul., 1955), pp. 92-96, Jstor.  
50. Correction: A Correction for the Trapezoidal Rule (in Classroom Notes)  
    J. J. Hart
    American Mathematical Monthly, Vol. 59, No. 6. (Jun. - Jul., 1952), p. 406, Jstor.  
51. A Correction for the Trapezoidal Rule (in Classroom Notes)  
    J. J. Hart
    American Mathematical Monthly, Vol. 59, No. 1. (Jan., 1952), pp. 33-37, Jstor.  

(c) John H. Mathews 2003