hw8 - Due: October 30, 2008 CS 257 (Luke Olson): Homework...

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Due: October 30, 2008 CS 257 (Luke Olson): Homework #8 Problem 1 Problem 1 Consider the integral Z 2 1 3 xe x 2 dx a. We want to approximate the integral using: (i) basic midpoint rule (ii) basic trapezoid rule (iii) basic Simpson’s rule Compute the absolute and relative errors for (i)-(iii) using the analytic solution to the integral and comment on the results b. Compare the absolute error with the theoretical bounds for (ii) and (iii) Problem 2 Repeat problem # 1 with composite rules for each using h = 0 . 1. Problem 3 Repeat problem # 1 with composite rules for each using h = 0 . 05. Page 1 of 2
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Due: October 30, 2008 CS 257 (Luke Olson): Homework #8 Problem 4 Problem 4 Consider the task of interpolating the Runge function on the interval -1 to 1, where the Runge function is f ( x ) = 1 1 + 25 x 2 a. Write a function called linear spline that takes in x and y and returns a piecewise polynomial of the degree 1 spline. You can do this easily using mkpp() in Matlab. You can use template linear
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This note was uploaded on 07/10/2011 for the course CS 257 taught by Professor Olson during the Spring '08 term at University of Illinois, Urbana Champaign.

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hw8 - Due: October 30, 2008 CS 257 (Luke Olson): Homework...

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