Day
|
Section
|
Topic
|
Assigned or Due
|
W 1/17
|
2.1, 2.2
(Also Trefethen notes.)
|
Introduction. Introduction by example.
|
A #1
|
F 1/19
|
|
Cont.
Program written in class: bob.m
|
|
M 1/22
|
|
Matlab
tutorial in class.
(Bring laptops!) Linear ODE example. In-class Matlab session: session012207.txt
|
|
W 1/24
|
|
Linear ODEs, cont.; Matlab tutorial cont.
edsODE.m session012407.txt
|
|
F 1/26
|
2.3 |
Standard heat problem:
exact solution by Fourier
series/separation of variables.
|
A
# 1 Due
A #2
|
M 1/29
|
2.4
|
Review
Taylor series. |
|
W 1/31
|
2.5
|
Standard
heat problem by explicit
method:
Truncation error. |
|
F 2/2
|
2.6 |
cont.;
Standard
heat problem by explicit
method: Maximum principle proof of convergence. |
A
# 2 Due
A #3
|
M 2/5
|
|
explicitfig.m
thomas.m
vera.m
|
|
W 2/7
|
2.7 |
Standard
heat problem by explicit
method:
Fourier analysis of stability. |
|
F 2/9
|
|
Example:
explicit method on
u_t = (1+2x) u_xx + c u
|
A
# 3 Due
|
M 2/12
|
2.8
& 2.9 |
Standard
heat problem by implicit method:
Scheme. |
A
# 3 Due |
W 2/14
|
2.12
|
Standard
heat problem by implicit method:
Analysis. Also Richardson method. |
A #4
|
F 2/16
|
2.10
|
"Theta
method" including Crank-Nicolson
ABOUT YOUR
PROJECT
|
|
M 2/19
|
|
cont.
|
|
W 2/21
|
2.11
|
Max
principle argument for "theta method". |
|
F 2/23
|
2.13
|
general
boundary conditions
|
A
# 4 Due |
M 2/26
|
|
uneven.m
implicitheat.m
imp2D.m
|
Project Proposal Due
A #5
|
W 2/28
|
|
general
boundary conditions, cont. |
|
F 3/2
|
2.15
|
most
general linear heat equation (in one spatial dimension); advection
|
|
M 3/5
|
|
cont.;
upwinding
|
A
# 5 Due
A
#5 SOLUTIONS
(I will hand out these on paper, but you can have an early look)
|
W 3/7
|
2.17
|
cont.;
divergence form
nonlinear diffusivity
|
A
#6 |
F 3/9
|
|
implementation:
passing functions, demonstrating convergence
a5prob4.m
manf.m
a5prob4c.m
|
|
3/12--3/16
|
|
Spring
Break
|
|
M 3/19
|
|
Guest
lecture (David Maxwell) on the finite element method.
|
|
W 3/21
|
|
Class cancelled
|
|
F 3/23
|
|
Class cancelled
nonlinheat.m
|
A
# 6 Due (at my box) |
M 3/26
|
4.1
|
pure
transport; characteristics
|
A
#7 |
W 3/28
|
4.2
|
cont.;
connection to classical wave equation; Burger's equation; upwinding; CFL
|
|
F 3/30
|
|
cont
|
Project Version 1.0
Due |
M 4/2
|
4.3
|
convergence
for upwinding
upwind.m
|
Project Version 1.0
Due |
W 4/4
|
4.4
|
phase
errors |
A
# 7 Due |
F 4/6
|
|
cont
|
A
# 7 Due
A
#8
Project Version 1.0
Due |
M 4/9
|
4.5
|
Lax-Wendroff
|
Project Version 1.0
Due |
W 4/11
|
|
cont
|
|
F 4/13
|
4.6 |
conservation
laws |
A
# 8 Due |
M 4/16
|
|
cont
lwfigure.m
upwindfigure.m
|
A
# 8 Due |
W 4/18
|
|
Class cancelled
|
|
F 4/20
|
|
Guest
lecture (Orion Lawlor): reaction-diffusion equations and images ...;
links:
Ice
solidification simulation in a Java applet.
Reaction-diffusion
equations for graphics textures.
PDEs
computed on the graphics card.
|
|
M 4/23
|
|
Special
topic: Chebyshev spectral methods.
classdemo042307.m
cheb.m
p9.m
p13.m
p19.m
Reference: L. N. Trefethen, Spectral Methods in MATLAB, SIAM
Press 2000; web.comlab.ox.ac.uk/oucl/work/nick.trefethen/spectral.html
|
|
W 4/25
|
6.1
|
cont.; elliptic problems by finite
difference
waveleap.m
see also from spring 2005:
brown.m
brownpot.m
heatbm.m
bvplinshoot.m
potentialcube.m
|
A
#9 (worth twice a usual assignment) |
F 4/27
|
|
UAF Spring Fest (no
classes) |
|
M 4/30
|
6.2
|
error
analysis for elliptic
|
|
W 5/2
|
6.3
|
general
diffusion
|
|
F 5/4
|
5.1, 5.2, 5.3
|
Lax equivalence theorem
|
|
M 5/7
|
|
|
|
Friday 5/11
|
|
TURN IN TO MY BOX BY 5:00 PM
|
Version 2.0
Due
A
# 9 Due
A#9 Solutions
|