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# HW_05 - ChE 348 Homework 5 Finite Differences 1 Suppose a...

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ChE 348 Homework # 5 _______________________________________________________________________ _ Finite Differences 1. Suppose a car is traveling on a straight road. Estimate (by hand) the speed of the car when t = 0. 4, and 8 sec with O( h 2 ), using the following times and positions. Time, sec 0 2 4 6 8 Distance, m 0 25 90 230 750 2. Write a computer program to find derivative of exp(- x ) at x = 0.5 using forward and backward difference representations of O( h ) and O( h 2 ) and central difference representations of O( h 2 ) and O( h 4 ). Use stepsizes h = 0.1 and 0.05. Compared the results with each other and with exact answer. (DO NOT USE BUILT-IN MATLAB FUNCTIONS) Gaussian Elimination 3. Solve (by hand) the following linear systems using Gaussian elimination and two- digit rounding arithmetic, with partial pivoting if necessary. Do not record the equations. (a) 4 x 1 + x 2 + 2 x 3 = 9, 2 x 1 + 4 x 2 x 3 = –5, x 1 + x 2 3 x 3 = –9. (b) x 1 x 2 + 3 x 3 = 2, 3 x 1 3 x 2 + x 3 = –1, x 1 + x 2 = 3. 4. Write a Gaussian elimination code and use it to solve the following systems of linear equations Ax = b (a) A = 8 7 7 7 6 7 6 6 5 5 6 5 4 4 4 5 , b = 29 25 21 17 The exact answer is

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HW_05 - ChE 348 Homework 5 Finite Differences 1 Suppose a...

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