HW2_spring10 - BIL108E 4-2 1 0 0-2 1-2 4-2 1 0 A= 0 1-2 4-2...

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Unformatted text preview: BIL108E 4 -2 1 0 0 -2 1 -2 4 -2 1 0 A= 0 1 -2 4 -2 1 0 1 -2 4 -2 0 IntroductiontoScientificandEngineeringComputing 0Homework2 -2 0 0 1 3 Spring10 1. The upward velocity of the rocket measured1with respect 1 time and the data is given in the is 3 -2 to 0 0 following table 4 -2 1 0 0 -2 Velocity vs time data for a rocket 4 -2 1 -2 1 0 B = t (s) Velocity, v (m/s) Time, 0 1 -2 4 -2 1 5 0 0 106.8 -2 4 -2 1 8 1 0 177.2 1 -2 0 3 12 279.2 Note that A is not diagonally dominant, but that does not necessarily preclude We wanted to approximate the velocity profile by convergence. Construct the set of linear equation and solve the equation for the coefficients the following equations: 2. 4 -1 0 0 0 0 0 1 0 x1 0 0 By taking u6= u4 -1 the following system of0equations x2 0 solve 4 -1 0 0 0 + 4u1 - u2 = +00.4 . 4 -1 0 0 0 0 x.3 0 0 . -1 . . . . . . . . . . . . . . . . = . . . . . . . . -u1 + 4u2 - u3 = . + 0.6 . 0.2 . 0 + 0.8 0 0 0 -1 4 -1 0 xn-2 0 -u2 + 4u3 - u4 = 0.4 0 -u3 + 4u4 - u5 = 0 + 1.0 0 0 0 -1 4 -1 xn-1 0 0.6 xn 100 1 0 -u4 + 4u5 - u6 = 0.8 + 0.8. 0 0 0 0 -1 4 17. Modify the program in Example 2.17 (GaussSeidel method) so that it will solve in Run the program with n = 20 and compare the number of iterations with Example 2.17. Modify the program in Example 2.18 to solve the equations in Prob. 17 by the 3. The edges of the square plate are kept at the temperatures shown in the following figure. conjugate gradient method. Run the program with n = 20. Assuming steady-state heat conduction, the differential equation governing the temperature T 19. in the interior is T = 00 1 2 5 8 3 6 9 18. T = 00 4 7 T = 100 0 T = 2000 2T 2T + =0 x 2 y 2 If this equation is approximated by finite differences using the mesh shown, we obtain the following algebraic equations for temperatures at the mesh points: T1 0 -4 1 0 1 0 0 0 0 0 T2 0 1 0 0 0 0 0 1 -4 1 T 100 1 -4 1 0 1 0 0 0 3 0 T4 0 1 0 0 -4 1 0 1 0 0 T =- 0 1 0 1 -4 1 0 1 0 5 0 100 0 1 0 1 -4 0 0 1 T6 0 200 0 0 0 1 0 1 -4 1 0 T 7 0 0 0 1 0 1 -4 1 200 0 T 300 0 0 0 0 0 1 0 1 -4 8 T9 Solve these equations. Due Date: April 5, 2010 ...
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This note was uploaded on 05/12/2010 for the course MATH 123 taught by Professor Sait during the Spring '09 term at Istanbul Technical University.

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