I have provide you GDB of MTH603 but be aware this is not complete, so please do not rely on this, include some more material in this text.
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There are two special properties of Simpson's rule. One is that because of the symmetric placement of the three grid points, with the center point coinciding with the Gaussian point, one extra degree of accuracy is obtained in the polynomial. The second is that by using an equally spaced grid in the extended Simpson's rule, the endpoints are shared, so that with n+1 points, we can perform n/2 Simpson's rules, and not (n+1)/3.
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Best Regards
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