part f:
To go from i to x use x=(i-1)*delta x, to go from j to t use t=(j-1)*delta t
The equation in part e, becomes a matrix equation in M[i,j] in terms
of M[i-1,j-1], M[i,j-1] and M[i+1,j-1].
Sample picture for part f
Left half for part h
There are a
pair of errors in the handout around part c. First there is a typo,
it should be U_1 - U_3/3^2 + U_5/5^2 - U_7/7^2 and not 3^3. Second
the series U_1 - U_3/3^2 + U_5/5^2 - U_7/7^2 + ... converges to a
triangle function, but it is 1.233700550 times the f(x) given. The
next picture illustrates the convergence.
Numerical Instability, delta t = 0.002 the onset.
Numerical Instability, delta t = 0.002 the big picture.
Numerical Instability, delta t = 0.010 the final picture.
Triangle function
-- Not part of the project.
Numerical Instability
-- Not part of the project, but the tag line.