Two-Point Gaussian Quadrature Rule

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Presentation transcript:

Two-Point Gaussian Quadrature Rule http://nm.MathForCollege.com

Background Trapezoidal Rule by undetermined coefficients http://nm.MathForCollege.com

Basis of the Two-Point Gaussian Quadrature Rule http://nm.MathForCollege.com

How do I find the 4 unknowns? The four unknowns x1, x2, c1 and c2 are found by assuming that the formula gives exact results for integrating a general third order polynomial Exact integral is http://nm.MathForCollege.com

This is what I get from the RHS! http://nm.MathForCollege.com

Equating exact value with formula Equating Equations the two previous two expressions yield http://nm.MathForCollege.com

So we get 4 simultaneous NLEs Since the constants a0, a1, a2, a3 are arbitrary http://nm.MathForCollege.com

Solution of 4 simultaneous NLEs http://nm.MathForCollege.com

Final Expression for 2-point Gauss Quadrature Rule http://nm.MathForCollege.com

THE END http://nm.MathForCollege.com