# Gauss legendre 3 point formula

**3**-term recurrence relation [17, (18.9.1)]:. The

**Legendre**-

**Gauss**Quadrature

**formula**or

**Gauss**-

**Legendre**quadrature is.

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**points**is transformed to the wave number domain using the Fast Fourier Transform.

**Gauss**-Lobatto-

**Legendre**(GLL) quadrature

**formulas**.

**point Gauss**-

**Legendre formula**Exact for polynomials up to and including degree 5 (because using 5th degree polynomial) Higher-order

**Gaussian**Quadrature * OSU/CSE 541 * -1 1 x f(0.775) f(-0.775) -0.775 0.775 f(0) Higher-order

**Gaussian**Quadrature * OSU/CSE 541 * Integrate from a = 0 to b = 0.8 Transform from [0, 0.8] to [-1, 1.

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**point Gauss**quadrature rule, the integral is approximated as = b a I f (x dx ≈c 1 f (x 1 ) +c 2 f ( x 2) There are four unknowns x 1 x 2 c 1 and c 2 These are found by assuming that the

**formula**gives exact results for integrating a general third order polynomial,

**3 3**2 f ( ) = 0 1.

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**Gauss**quadrature. The transformed function can be evaluated at -1/\sqrt{3} to be equal to 0.516741 and at 1/\sqrt{3} to be equal to 1.305837. Therefore, the integral according to Eq. (22.23) is. I \cong 0.516741 + 1.305837 = 1.822578.