Ed Bueler: felb@uaf.edu, x7693
Office: Chapman 301C ( Hours)
Class times and rooms:
MWF 10:30-11:30 GRUE 206
Required Text: Morton & Mayers, Numerical Solutions of Partial
Differential Equations, Cambridge University Press 1994
Four other
texts are recommended,
of which two are freely available a page at a time:
- W. Press, et al., Numerical
Recipes in C (or Numerical
Recipes in Fortran), Cambridge University Press 1992. $55
at Amazon. Pages available free online at http://www.library.cornell.edu/nr/.
- C. Moler, Numerical
Computing
with MATLAB, SIAM Press 2004. $43. Pages
available free online at http://www.mathworks.com/moler/.
- D. Higham and N. Higham, MATLAB
Guide, SIAM Press 2000.
- S. Farlow, Partial
Differential Equations for Scientists and Engineers, Dover
1993. $11 at Amazon.
Syllabus Here
ABOUT YOUR
PROJECT
FAQ:
Replies to some Frequently Asked Questions
LINKS:
COMMENT on programming languages:
One free alternative to MATLAB
is the mathematical and scientific support built around the Python
scripting language, especially SciPy. Python
allows a programmer to work in the same kind of prototyping mode as MATLAB
but with much more powerful tools for major projects on supercomputers
and clusters. (As an environment to do the assignments in Math
615, however, this route is only recommended for experienced
Unix-familiar programmers. I am not one.)
Another free alternative is Octave,
an attempt to duplicate the functionality of MATLAB. I am sceptical that it is
well-supported in 2005, however.)
GRADING of Project Version 1.0:
Thirty (30) points were awarded for evidence of appropriate
progress. Another 30 points were awarded for the quality of the
exposition, analysis, and computation achieved so far. The total
was 60 points. ( Note that the
proposal was worth 20 points and Version 2.0 will be worth 120 points,
for a total of 200 points.)
|
Schedule: (my
planning document, version 11/06
re-edited)
Day
|
Section
|
Topic
|
Assigned or Due
|
F 1/21
|
|
intro; Taylor's thm with remainder
|
A #1
|
M 1/24
|
|
Taylor cont
|
|
W 1/26
|
|
ODE review
|
|
F 1/28
|
|
MATLAB intro by example; m-file: mysimp.m ; text file with command history: simpcommands.txt; also, comments on
passing functions to ode45: odecomments.txt
|
|
M 1/31
|
2.2, 2.3
|
heat equation and solution by Fourier series
|
A #1 Due
|
W 2/2
|
2.4, 2.5
|
an explicit method for the heat
equation
Q&A re problem #2 on A#2 (2.1 in text): a2comments.txt
|
A#2
|
F 2/4
|
|
more MATLAB; text file with in-class session: session
|
|
M 2/7
|
|
explicit for heat, cont.; truncation error and
consistency; my code for figure 2.2:
explicitfig.m
|
A #2 Due
|
W 2/9
|
2.6
|
convergence (by a maximum principle argument)
|
|
F 2/11
|
2.7
|
stability; Fourier analysis of modes on the
grid
|
A#3 |
M 2/14
|
|
D. Maxwell on
FEM
(references:
1.
Dietrich Braess, Finite
Elements: Theory, fast solvers, and applications in solid mechanics,
Cambridge U. Press 2001
2.
C. Johnson, Numerical
solution of partial differential equations by the finite element method,
Cambridge U. Press 1992)
|
|
W 2/16
|
2.8
|
brainstorming
on finite difference methods; implicit method for heat equation
|
A#4
|
F 2/18
|
2.9
|
solving
tridiagonal systems (e.g. from implicit method); use of sparse;
my code for figure 2.4:
expliciterr.m |
A #3 Due
|
M 2/21
|
2.10
|
Crank-Nicolson
and the "theta" methods;
ABOUT YOUR PROJECT
|
|
W 2/23
|
|
MATLAB show-and-tell;
truncation error for Crank-Nicolson; note
on definitions; session
on logical indexing
|
|
F 2/25
|
2.11
|
maximum
principle for certain theta methods; who cares?; heatmovie.m uneven.m
implicit.m
|
A #4
Due
A#5
|
M 2/28
|
2.13
|
general
boundary conditions; implementation thereof
|
|
W 3/2
|
2.15
|
a general
linear parabolic (heat-like) equation; relative sizes of conduction and
advection coefficient produces stability condition
|
|
F 3/4
|
|
cont.
note on convergence of explicit
method
|
A#6 REVISED
PROJECT PROPOSAL
DUE |
M 3/7
|
|
cont.;
max. principle in case of self-adjoint form
|
A #5
Due
|
W 3/9
|
2.17 |
nonlinear;
explicit method and adaptive time-stepping; "method of manufactured
solutions" |
|
F 3/11
|
4.1
|
characteristics
for transport equations
|
|
3/14-- 3/18
|
|
SPRING BREAK
|
|
M 3/21
|
|
more
on characteristics
nonlinheat.m, boundaryCN.m
|
A #6
Due
A#7
|
W 3/23
|
4.2, 4.3
|
f. d.
methods for transport upwind GOOD
|
|
F 3/25
|
|
cont.,
centered BAD |
|
M 3/28
|
4.4, 4.5
|
cont,
Lax-Wendroff BETTER
nonlinverif.m, upwind.m
|
A #7
Due
|
W 3/30
|
4.6, 4.7
|
Lax-Wendroff
for (nonlinear) conservation laws; Box method
|
|
F 4/1
|
4.8,
4.9, 4.10, 4.11
|
overview
of other schemes and issues
|
PROJECT V.
1.0 DUE; grading explanation
at left |
M 4/4
|
6.1
|
elliptic
problems (e.g. Poisson and potential)
|
A#8
|
W 4/6
|
|
elliptic,
cont.: potential.m, poterrs.jpg
[update: potential2.m ]
|
|
F 4/8
|
6.3
|
general
diffusion form:
diffusion.m usediff.m
[update: diffusion2.m usediff2.m ]
upwindfigure.m
|
A #8
Due
|
M 4/11
|
|
INTERLUDE:
Brownian motion(!)
brown.m brownpot.m
bvpfd.m
|
A#9
|
W 4/13
|
|
INTERLUDE:
method of lines
molexample.m molmanuf.m
|
|
F 4/15
|
|
method
of lines, cont.; stiffness for systems of ODEs
|
|
M 4/18
|
3.1, 3.2
|
two
spatial dimensions for heat equation; ADI
|
A #9
Due
|
W 4/20
|
|
ADI
cont.
heatbm.m
bvplinshoot.m
potentialcube.m
|
A#10
(first problem revised)
|
F 4/22
|
|
INTERLUDE:
ice flow
|
|
M 4/25
|
|
INTERLUDE:
minimal surface equation
minimal.m usemin.m usemin_smart.m
also (updates):
potential2.m, diffusion2.m, usediff2.m
|
|
W 4/27
|
4.6 |
INTERLUDE:
spectral methods
badinterp.m goodinterp.m
bvpcheb.m
(NEEDS: cheb.m; see also
p33.m; both from reference:
L. N.
Trefethen,
Spectral Methods in MATLAB, SIAM 2000)
|
|
F 4/29
|
|
Nanook
SpringFest (no classes) |
|
M 5/2
|
|
spectral
methods, cont.
|
|
W 5/4
|
6.2
|
error
analysis for potential equation
|
|
F 5/6
|
5.1,
5.2, 5.3, 5.4, 5.5 |
Lax
equivalence theorem |
|
5/9--
5/12
|
|
FINALS
|
PROJECT V.
2.0 DUE WED 5/11 AT 5:00 PM
A #10
Due THURS 5/12 at 5:00 pm
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