Numerical Integration using chained Gauss-Legendre
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03-21-2016, 05:51 PM
(This post was last modified: 01-16-2020 08:35 AM by Namir.)
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Numerical Integration using chained Gauss-Legendre
Back last year, a member of this website pointed to the simplicity of using the Gauss-Legendre quadrature (with a 3rd order Legendre polynomial) with vintage and new HP calculators. This prospect made me think of using a "chained" version of that type of quadrature to yield relatively good results. Here are my preliminary results usin Excel VBA.
The following Excel VB Code compares the chained Simpson's rule with a "chained" Gauss-Legendre quadrature using a 3rd order Legendre polynomial. The following is the configuration contents of the Excel sheet: Code: Cell Contents Here is the VBA code: Code: Function Fx(ByVal sFx As String, ByVal X As Double) As Double As you experiment with different functions and integration ranges, you should see that the chained Gauss-Legendre quadrature is significantly more accurate than Simpson's rule. Both methods use three points per divided interval. Enjoy! Namir |
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Numerical Integration using chained Gauss-Legendre - Namir - 03-21-2016 05:51 PM
RE: Numerical Integration usined chained Gauss-Legendre - Tugdual - 03-22-2016, 06:40 AM
RE: Numerical Integration usined chained Gauss-Legendre - lcwright1964 - 03-29-2016, 10:13 PM
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