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Shovelton's Rule

Let the values of a function f(x) be tabulated at points x_i equally spaced by h=x_(i+1)-x_i, so f_1=f(x_1), f_2=f(x_2), ..., f_(11)=f(x_(11)). Then Shovelton's rule approximating the integral of f(x) is given by the Newton-Cotes-like formula

int_(x_1)^(x_(11))f(x)dx=5/(126)h[8(f_1+f_(11))+35(f_2+f_4+f_8+f_(10)) +15(f_3+f_5+f_7+f_9)+36f_6].

See also

Boole's Rule, Hardy's Rule, Newton-Cotes Formulas, Simpson's 3/8 Rule, Simpson's Rule, Trapezoidal Rule, Weddle's Rule

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References

King, A. E. "Approximate Integration. Note on Quadrature Formulae: Their Construction and Application to Actuarial Functions." Trans. Faculty of Actuaries 9, 218-231, 1923.Sheppard, W. F. "Some Quadrature-Formulæ." Proc. London Math. Soc. 32, 258-277, 1900.Whittaker, E. T. and Robinson, G. The Calculus of Observations: A Treatise on Numerical Mathematics, 4th ed. New York: Dover, p. 151, 1967.

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Shovelton's Rule

Cite this as:

Weisstein, Eric W. "Shovelton's Rule." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ShoveltonsRule.html

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