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mae107 hw6 - MAE 107 Homework 6 Numerical Methods in...

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MAE 107 - Homework # 6 Numerical Methods in Engineering Prof. Alison Marsden Due date: Monday May 16, 2011 Problem 1 The following tridiagonal system must be solved as part of a larger algorithm (Crank-Nicolson) for solving partial differential equations: 2 . 01475 - 0 . 020875 - 0 . 020875 2 . 01475 - 0 . 020875 - 0 . 020875 2 . 01475 - 0 . 020875 - 0 . 020875 2 . 01475 × T 1 T 2 T 3 T 4 = 4 . 175 0 0 2 . 0875 Use the Thomas algorithm (develop a code in Matlab) to obtain a solution. Problem 2 Recall from HW 4, Problem 8, that the following system of equations is designed to determine concentrations (the c ’s in g / m 3 ) in a series of coupled reactors as a function of the amount of mass input to each reactor (the right-hand sides in g/day), 15 c 1 - 3 c 2 - c 3 = 3300 - 3 c 1 + 18 c 2 - 6 c 3 = 1200 - 4 c 1 - c 2 + 12 c 3 = 2400 Solve this problem with the Gauss-Seidel method to s = 5% using Matlab (you need to write a function that performs Gauss- Seidel). Problem 3 Repeat Problem 2, but use Jacobi iteration (again, you need to implement this method in Matlab).
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