hw8107

hw8107 - MAE 107 - Homework # 8 Numerical Methods in...

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Unformatted text preview: MAE 107 - Homework # 8 Numerical Methods in Engineering Prof. Alison Marsden Due date: Friday June 3, 2011 Problem 1- Time step choice for stiff Euler Given d y d t =- 100 , 000 y + 99 , 999e- t (1) (a) Estimate the step-size required to maintain stability using the explicit Euler method. (b) If y (0) = 0, use the implicit Euler to obtain a solution from t = 0 to 2 using a step size of 0.1. Problem 2 - Lorenz system Use MATLAB to integrate d x d t =- x + y d y d t = rx- y- xz (2) d z d t =- bz + xy where = 10 , b = 2 . 666667 , and r = 28. Employ initial conditions of x = y = z = 5 and integrate from t = 0 to 20. Problem 3 - Stiff system The following system is a classic example of stiff ODEs that can occur in the solution of chemical reaction kinetics: d c 1 d t =- . 013 c 1- 1000 c 1 c 3 d c 2 d t =- 2500 c 2 c 3 (3) d c 3 d t =- . 013 c 1- 1000 c 1 c 3- 2500 c 2 c 3 1 Solve these equations in MATLAB from t = 0 to 50 with initial conditions c 1 (0) = c 2 (0) = 1 and c 3 (0) = 0...
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hw8107 - MAE 107 - Homework # 8 Numerical Methods in...

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