MATH 566
Spring 2009
Homework
5.1
1b, 4ab, 8ab
5.2
2d - In addition solve with h=0.1 and give your solution in the form of a table with columns t and w(t)
4d - compare by plotting the actual error and the error bound on the same graph for both values of h
16 - In addition solve for t=0.01j, and plot the current vs. time
5.4
2d, 14d, 27, 28
5.6
1d - Only use the four step method 5.34
5d - i.e. implement the four step predictor-corrector method using 5.34 and 5.37
12
5.10
5, 7
5.11
11, 12, 15
7.1
2c, 3b, 5cd, 9
7.2
3be, 7be, 9, 13 (show in your own words, don't copy solution from the back of the book), 14
7.3
5bc, 7bc, 17
7.3
21, 24, 25
7.5
7bc, 8bc, 9(i)(iii)
11.1
7
11.2
6
11.3
7
11.4
6
12.1
Problem 1: 3c, and verify order of convergence by calculating the rms error on at least 7 different grids.
Problem 2: Construct the system of finite difference equations (Ax=b) for the Poisson problem when the spacing in the x and y directions are not necessarily equal. Use second order central differences and Dirichlet boundary conditions.
12.2
Determine the stability of the second order centered difference (in space and time) method discused in class, 15, 18
12.3
8
12.4
Attached problem on the finite element method