Computes progressive,
tabular values of the integral Y(x) =
∫ax
f(t) dt, for varying x,
a ≤ x ≤ b, by the selected method of
numerical integration, the trapezoidal or
the Simpson's rule. The integration step is
h = s ⁄ n.
The case solved is
the standard Gaussian integral, i.e.,
ΔΦ(x) = ∫ax
φ(t) dt (a ≤ x ≤ b),
but the method is general.
This case was chosen to permit the comparison with tables published
or easily obtained, e.g., from
Excel(.xls).
A table is made for x = a(s)b,
and curves are drawn (with all the nodes computed)
for the numerical integral and its error (from the known analytical solution).
Possibly, the numerical and analytical curves are visually
indistinguishable. |
• Weisstein, Eric W. "Numerical
integration". From MathWorld—a Wolfram web resource.
• Wolfram Mathematica
Online Integrator.
• Atkinson [1985]; Conte & de Boor [1980]; Greenspan & Casulli [1988].
• Scheid, Francis,
1991, "Análise Numérica",
McGraw-Hill de Portugal, Lisboa (Portugal).
ISBN 972-9241-19-8.
• Search numerical integration...
• Numerical methods (bibliography: "Eric's Scientific Book List",
Eric Weisstein).
• Euclidean
algorithm for gcd (lcm) (Wikipedia).
• 1860-05-03: Volterra, Vito (1940-10-11). |
