ASE311 HW 2 pdf - Part II 3[False-position ±ormula Let ±...

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ASE 311 Engineering computation, Fall 2009, Homework 2 Due: Friday, September 11, 2:00 PM in the lecture room JGB 2.216 Report all work, including any m -fles you have written. You may also fnd the command diary use±ul in recording your MATLAB session. Please write clearly and be sure to label ±or which problem each solution is. Please, staple Part I and Part II separately and make sure that your name is written on both parts. Part I 1. [Chapra, Problem 4.12] Use zero- through third-order Taylor polynomials at the point u = 1 to predict U (3) ±or U ( u ) = 25 u 3 6 u 2 + 7 u 88 Compute the true relative error in percent ±or each approximation. Use MATLAB ±or evaluations i± necessary. 2. Using MATLAB , plot the Taylor polynomials ±rom the previous exercise together with the ±unction U in the same fgure. Use the interval [ 1 , 3].
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Unformatted text preview: Part II 3. [False-position ±ormula] Let [ ±, ² ] an interval and U a ±unction such that U ( ± ) U ( ² ) < 0. What is the equation o± the straight line that passes through the points ( ±, U ( ± )) and ( ², U ( ² ))? Find the intersection o± that line with the u-axis. 4. [Square root o± 2 by the bisection method] Find the positive zero o± the ±unction U ( u ) = u 2 − 2 using MATLAB . Apply the bisection method starting ±rom the interval [0 , 3]. What is the approximate relative error in percent a±ter ten iterations? Compare with the true error. 5. [Square root o± 2 by the ±alse position method] Repeat the previous exercise, but use the ±alse-position ±ormula instead o± bisection to estimate the root. Which method is better in this case?...
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  • Spring '08
  • Taylor Polynomials, Complex number, Root-finding algorithm, Bisection Method, lecture room JGB, third-order Taylor polynomials

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