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trapezoidal rule


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1: 7.22 Methods of Computation
Additional references are Matta and Reichel (1971) for the application of the trapezoidal rule, for example, to the first of (7.7.2), and Gautschi (1970) and Cuyt et al. (2008) for continued fractions. …
2: 3.5 Quadrature
§3.5(i) Trapezoidal Rules
The elementary trapezoidal rule is given by … The composite trapezoidal rule is … Similar results hold for the trapezoidal rule in the form …
Table 3.5.20: Composite trapezoidal rule for the integral (3.5.45) with λ = 10 .
h erfc λ n
3: 8.25 Methods of Computation
See Allasia and Besenghi (1987b) for the numerical computation of Γ ( a , z ) from (8.6.4) by means of the trapezoidal rule. …
4: 9.17 Methods of Computation
The trapezoidal rule3.5(i)) is then applied. …
5: Bibliography
  • G. Allasia and R. Besenghi (1987a) Numerical computation of Tricomi’s psi function by the trapezoidal rule. Computing 39 (3), pp. 271–279.
  • G. Allasia and R. Besenghi (1991) Numerical evaluation of the Kummer function with complex argument by the trapezoidal rule. Rend. Sem. Mat. Univ. Politec. Torino 49 (3), pp. 315–327.
  • G. Allasia and R. Besenghi (1987b) Numerical calculation of incomplete gamma functions by the trapezoidal rule. Numer. Math. 50 (4), pp. 419–428.
  • G. Allasia and R. Besenghi (1989) Numerical Calculation of the Riemann Zeta Function and Generalizations by Means of the Trapezoidal Rule. In Numerical and Applied Mathematics, Part II (Paris, 1988), C. Brezinski (Ed.), IMACS Ann. Comput. Appl. Math., Vol. 1, pp. 467–472.
  • 6: 13.29 Methods of Computation
    In Allasia and Besenghi (1991) and Allasia and Besenghi (1987a) the high accuracy of the trapezoidal rule for the computation of Kummer functions is described. …
    7: 3.4 Differentiation
    The integral on the right-hand side can be approximated by the composite trapezoidal rule (3.5.2). … As explained in §§3.5(i) and 3.5(ix) the composite trapezoidal rule can be very efficient for computing integrals with analytic periodic integrands. …