Homework assignments are from Numerical Mathematics and Computing, Seventh Edition, by Ward Cheney and David Kincaid, Brooks/Cole Publishing Co., 2013.

Day Date Problems Due Computer Problems Due
Wed 1/23 1.1: 1, 2, 6, 8, 9, 12
1.2: 1, 4, 8, 28
 
Fri 1/25 1.3: 5, 8a, 8e  
Mon 1/28   1.2: 14
Introduction to Octave
Loss of Significance
Wed 1/30 2.1: 5, 6  
Fri 2/1 2.2: 2

Use gauss.m and solve.m to solve at least one 5×5 linear system. The matrix A, a known solution vector x and the right-hand-side vector b can be created with

A = round(20*rand(5,5))
x = [1:5]'
b = A*x
Mon 2/4   2.3: 4, 5
Wed 2/6 3.1: 12 Code bisection and test on  2 
Fri 2/8 3.2: 6 (okay to use octave) 3.2: 10
Mon 2/11 3.3: 5, 14  
Wed 2/13 4.1: 1, 10  
Fri 2/15 4.1: 18
4.2: 2, 9
 
Mon 2/18 4.3: 6, 7 4.3: 3, 4
Wed 2/20 5.1: 11  
Fri 2/22 5.1: 14, 15 5.1: 4
Mon 2/25 5.2: 2, 10, 15  
Wed 2/27 5.3: 3a, 3b, 3c, 4  
Mon 3/4 6.1: 3, 17  
Mon 3/18 6.2: 7, 8  
Wed 3/20 7.1: 12 7.1: 2a
Fri 3/22 7.2: 3, 12  
Mon 3/25 7.3: 8 (use x(0)=1+ε for the initial condition)  
Wed 3/27   7.3: 4 (Show how to derive the formulas and code a procedure that uses them.)
Fri 3/29   7.4: 3, 6
Mon 4/1 8.1: 6a, 6b, 6e, 16 (watch for typo)  
Wed 4/3   8.4: 1a, 1b (use Jacobi and Gauss-Seidel to solve.)
Fri 4/5 9.1: 3, 16  
Mon 4/8 9.2: 8, 9  
Wed 4/10 9.3: 8  
Fri 4/12 10.1: 2 10.1: 7
Mon 4/15   10.2: 2 (use 1600 and 3200 instead of 16000 and 32000), 6, 13
Wed 4/17   10.3: 5, 17
Wed 4/24 11.1: 1a, 7  
Fri 4/26 11.2: 5, 8  
Wed 5/1 12.1: 1, 8

Solve the following two problems by modifying and running a copy of crank_nicolson:

  1. ut = 0.1 uxx,     0 ≤ t ≤ 2
    u(0,t) = 100
    u(1,t) = 0
    u(x,0) = 0

  2. ut = 0.01 uxx,     0 ≤ t ≤ 20
    u(0,t) = 100et
    u(1,t) = 0
    u(x,0) = 100(1−x)

Note that ut means the first partial derivative of u with respect to t and uxx means the second partial derivative of u with respect to x.

Mon 5/6 12.3: 3