hw18 - (6.22) and the second equation From the bottom on...

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MAE 107 Assignment 8 Due Tuesday, 22 Nov., 2010 1. Epperson, Section 6.3 problem: 2b. Note that the defnition oF the notation in the problem is: b y ′′ b , [0 , 1] = max t [0 , 1] | y ′′ ( t ) | . 2. ±or this same problem, assume that you start Euler’s method with the correct value, i.e., y 0 = y ( t 0 ), and that you are solving the ODE over [0 , 1]. ±ind a bound on e euler h = max k | y k y ( t k ) | . Hint: Use the Fact that y ( t ) = f ( t, y ( t )), and di²erentiate. 3. Write matlab code For the predictor-corector trapezoid method, and apply it to y = sin( t + y ) e 1+ y 2 with y (0) = 2. Solve the problem over t [0 , 2]. Do this For numbers oF steps n = 2, 4, 10, 100, 1000 and 2000. Plot log 10 oF the error versus log 10 oF n . Also plot log 10 oF the error versus log 10 oF the number oF Function evaluations. You may use the solution From the predictor- corector trapezoid method with n = 2000 as the true solution, and only go up to n = 1000 in the plots. 4. Epperson, Section 6.4 problem: 1. (ReFer to the indicated equation
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Unformatted text preview: (6.22) and the second equation From the bottom on page 187.) For full credit, make sure to fully “comment” all your matlab codes as indicated in the examples given in the very bottom bullet on the website. All the above problems (iF graded) are worth 5 points each, with the exception oF Problem 3, which is worth 10 points. You must show your work and/or provide copies oF the code(s) For each problem in order to receive Full credit. Study Problems (Will not be graded.) 1 • Do problems 1 and 2 above, but with y ′ = sin( t + y ) e − √ 1+ y 2 . • Write your own matlab code for the fourth-order Runge-Kutta method. Apply this to Problem 3 above, and add the new data to the plots. • Epperson, Section 6.6 problem: 1a. 2...
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This note was uploaded on 01/15/2012 for the course MAE 107 taught by Professor Rottman during the Spring '08 term at UCSD.

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hw18 - (6.22) and the second equation From the bottom on...

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