assignment_3[1]

Assignment_3[1] - formula with Richardson extrapolation for the derivative and Romberg integration for the integral The data fo h h x dx ′ r

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Math 400 Assignment #3 -- Numerical Integration and Differentiation 1 2 3 Find the exact values of the Gauss points 1 1 and weights for 3. x x x n - < < < < = 1. 7 Estimate each of the following integrals to seven decimal place accuracy (absolute error less than 10 ) using Gaussian quadrature, the trapezoidal method, and Romberg integration. For each method sta - ( 29 1 2 0 te how many points were needed to achieve the desired accuracy. Also provide a graph of each function over an interval that includes the interval of integration. a) sin 2 x dx π ( 29 ( 29 ( 29 2 2 2 1 1 1 b) 2 sin 2 if 0 c) 2 , where 2 2 1 if 0 x e dx x x Sinc x dx Sinc x x x - - = = 2. ( 29 ( 29 1.8 1 Estimate 1.4 and as accurately as you can using the centered difference
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Unformatted text preview: formula with Richardson extrapolation for the derivative, and Romberg integration for the integral. The data fo h h x dx ′ ∫ r the function is given in the following table: 4. ( 29 1.0 0.24197072 1.1 0.21785218 1.2 0.19418605 1.3 0.17136859 1.4 0.14972747 1.5 0.12951760 1.6 0.11092083 1.7 0.09404908 1.8 0.07895016 x h x ( 29 ( 29 2 2 1 2 20 For the function use the centered difference formula with 10 , 10 , , 10 2 to create a table of estimates of 1.4 . Include a column for the relative error of each estimate. x e g x h g----= = ′ … 3. Due: April 20, 2010...
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This note was uploaded on 09/16/2011 for the course MATH 400 taught by Professor Staff during the Spring '11 term at S.F. State.

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