Difference between revisions of "Length of a curve using numerical methods"
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Instead of evaluating this integral with a table, a numerical method called Simpson's rule can be used: | Instead of evaluating this integral with a table, a numerical method called Simpson's rule can be used: | ||
| − | + | the length of the curve after n iterations = L<sub>n</sub> = (<span>Δ</span>x/3)(f(x<sub>0</sub>) + 4f(x<sub>1</sub>) + 2f(x<sub>2</sub>) + 4f(x<sub>3</sub>) +2f(x<sub>4</sub>) + ...+ 2f(x<sub>n-2</sub>) + 4f(x<sub>n-1</sub>) + f(x<sub>0</sub>)) | |
where <span>Δ</span>x = (b-a)/n with a and b being the boundaries and n the number of iterations of the calculation. | where <span>Δ</span>x = (b-a)/n with a and b being the boundaries and n the number of iterations of the calculation. | ||
Revision as of 18:41, 1 April 2021
Simpson's Rule is used to calculate integrals numerically.
From the Length of curve page, the length can be calculated using the integral: ∫sqr(1+f '(x)2)dx
Instead of evaluating this integral with a table, a numerical method called Simpson's rule can be used:
the length of the curve after n iterations = Ln = (Δx/3)(f(x0) + 4f(x1) + 2f(x2) + 4f(x3) +2f(x4) + ...+ 2f(xn-2) + 4f(xn-1) + f(x0))
where Δx = (b-a)/n with a and b being the boundaries and n the number of iterations of the calculation.
