HW_06 - x xy x Use each of the initial guesses x y =(1.2...

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ChE 348 Homework # 6 _______________________________________________________________________ _ Iteration Methods 1. Write a computer code that does Gauss-Seidel for the following problem, for a specified number of iterations. How many iterations does it take to get convergence, in the sense that the consecutive iterates differ by less than 10 -6 ? A = - - - - - - - - - - 79 49 16 32 5 49 47 5 2 3 16 5 36 15 9 32 2 15 52 14 5 3 9 14 14 and b = (-15, -100, 106, 329, 463) T . The correct answer is x = (0, 1, 2, 3, 4) T . Nonlinear System: Newton’s Method 2. Consider the nonlinear system, 1 9 1 2 1 9 1 2 = + + - - = + - - - y x e y x e y x Take ( x 0 , y 0 ) = (1, 1) and do two iterations of Newton’smethod; you should get ( x, y ) = (-0.4232, 0.2527) 3. Write a computer code to solve the following systems, using Newton’s method (a) 1 4 2 2 2 2 = - = + y x y x True solutions: ) 5 . 1 , 5 . 2 ( ± ± (b) 96 . 1 4 . 0 4 4 2 2 2 - - = = + x x y y x One of the roots: (1.77017, 0.46543) (c) ) 0 , 0 , 0 ( ) , , ( . 0 ) 3 10 ( 3 1 20 , 0 1 2 625 4 , 0 5 . 0 ) cos( 3 0 0 0 2 2 = = - + + = - + - = - - - z y x use z e y y x yz x xy π 4. Find all solutions to the system 4 3 9 3 2 3 2 = - = + y y
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Unformatted text preview: x xy x Use each of the initial guesses ( x , y ) = (1.2, 2.5), (-2, 2.5), (-1.2, -2.5), (2, -2.5). Observe the root to which each of the iterations conserves and the number of iterates computed. Comment on your results. 5. Find the equilibrium conversion of the following reactions using Newton’s method. 2 2 4 2 1 10 4 10 5 2--× = = ↔ + × = = ↔ + D A C B A C C C C K C D A C C C K C B A Initial concentrations are C A,0 = 40 C B,0 = 15 C C,0 = 0 C D,0 = 10 All concentrations are in kmol/m 3 . (Hint) For the conversions of x 1 and x 2 , the concentrations of the components can be calculated as: 1 , 21 2 1 , 2 , 1 , 1 , 1 2 1 , 2 , 1 , 10 10 ) 1 ( 10 15 15 15 ) 1 ( 10 30 40 2 x C x C x x C x C x C C x C x C x x C x C x C C D D D B C C B B D B A A-=-= + = + + =-=-=--=--=...
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This note was uploaded on 02/22/2010 for the course CHE 348 taught by Professor Chelikowsky during the Spring '08 term at University of Texas.

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HW_06 - x xy x Use each of the initial guesses x y =(1.2...

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