Computes progressive,
tabular values of the integral Y(x) =
∫ax
f(t) dt, for a ≤ x ≤ b,
by the selected method of numerical integration, trapezoidal or
Simpson's rule. The integration step is
h = s ⁄ n.
The case shown is the standard Gaussian integral, i.e.,
Φ(Z) = ∫−∞Z
φ(t) dt,
for 0 ≤ z ≤ Z
(with 0.5 added to Φ), but the method is general.
The case was chosen to permit the comparison with tables published
or easily obtained, e.g., from
Excel(.xls).
A table is made for z = 0(s)Z, and curves
are drawn for the numerical integral and its error (from
Φ = [1 + erf(z⁄√2)] ⁄ 2). |
• Weisstein, Eric W. "Numerical
integration". From MathWorld—a Wolfram web resource.
• Wolfram Mathematica
Online Integrator.
• Atkinson, Kendall,
1985, "Elementary numerical analysis",
John Wiley & Sons, New York, NY (USA).
ISBN 0-471-82983-8.
• Conte, Samuel D., and
Carl de Boor,
1980 (1987), "Elementary numerical analysis",
McGraw-Hill, Singapore.
ISBN 0-07-066228-2.
• Scheid, Francis,
1991, "Análise Numérica",
McGraw-Hill de Portugal, Lisboa (Portugal).
ISBN 972-9241-19-8.
• Greenspan, Donald,
Vincenzo Casulli,
1988, "Numerical analysis
for applied mathematics, science, and engineering",
Addison-Wesley, Redwood City, CA (USA).
ISBN 0-201-09286-7 (QA297.G725).
• Search numerical integration...
• Numerical methods (bibliography: "Eric's Scientific Book List",
Eric Weisstein).
• Euclidean
algorithm for gcd (lcm) (Wikipedia).
• 1903-04-25: Kolmogorov, Andrey Nikolaevich
(1987-10-20). |
