Ed Bueler: 474-7693
elbueler@alaska.edu
Office: Chapman 301C ( hours)
Class times and room:
MWF 9:15 -- 10:15 am
Gruening 401
CRN: 36278
Required text:
R. J. LeVeque, Finite Difference Methods for Ordinary and Partial Differential Equations,
SIAM Press 2007 (ISBN-13: 978-0-898716-29-0)
Links:
Matlab/Octave codes:
Python codes:
|
Schedule: (version 6 May 2017)
Thanks to all students for making this a nice semester!
Solutions to the final were sent by email, but I've posted the codes from the solutions here;
see the chronological listing of Matlab/Octave codes below left.
| Day |
Sections |
Topic |
Assigned / Due |
| W 1/18 |
|
intro by example: heat equation |
Assignment #1 |
| F 1/20 |
|
"laptop day": learn some Matlab/Octave |
|
| M 1/23 |
1.1 |
Taylor's theorem |
|
| W 1/25 |
|
cont. |
Assignment #2 |
| F 1/27 |
1.2, 1.3, 1.4 |
finite differences |
A#1 DUE |
| M 1/30 |
2.1, 2.2, 2.3, 2.4 |
ODE BVPs (e.g. steady heat) by FD
code in-class: steve.m |
|
| W 2/1 |
|
error; verification cases; FD for u'''
code in-class: dave.m |
|
| F 2/3 |
2.5,2.6 |
truncation error |
|
| M 2/6 |
2.7, 2.8, 2.9 |
convergence, consistency, stability, and the "fundamental theorem" |
A#2 DUE
Assignment #3 |
| W 2/8 |
|
in-class projects
worksheets: Project A, Project B |
|
| F 2/10 |
|
projects finished |
|
| M 2/13 |
|
matrix norms |
|
| W 2/15 |
2.16 |
nonlinear ODEBVPs and Newton's method |
A#3 DUE |
| F 2/17 |
2.10 |
stability |
A#3 DUE
Assignment #4 |
| M 2/20 |
2.11, 2.12, 2.13, 2.14, 2.15 |
Green's functions, Neumann boundary conditions |
|
| W 2/22 |
3.1, 3.2, 3.3 |
Poisson equation in 2D |
|
| F 2/24 |
3.4, 3.5, 3.6, 3.7 |
cont.
slides on classical iterative methods: iterative.pdf |
A#4 DUE
Assignment #5 |
| M 2/27 |
|
Bueler traveling |
MIDTERM EXAM |
| W 3/1 |
|
Bueler traveling |
|
| F 3/3 |
|
Bueler traveling |
|
| M 3/6 |
5.1 |
ODE IVPs |
|
| W 3/8 |
5.2 |
integral equations, Picard iteration, Lipschitz constant |
A#5 DUE
Assignment #6 |
| F 3/10 |
5.3 |
matrix exponential and Duhamel |
|
| 3/13--17 |
|
no classes: Spring Break |
|
| M 3/20 |
5.4, 5.5, 5.6, 5.7 |
methods for ODE IVPs: forward/backward Euler and trapezoid; truncation error |
A#6 DUE |
| W 3/22 |
|
MIDTERM QUIZ
(rescheduled)
review guide for Midterm Quiz |
MIDTERM QUIZ |
| F 3/24 |
5.8, 5.9 |
methods cont.
code in-class: circling.m |
Assignment #7 |
| M 3/27 |
|
preview: method of lines for PDEs, and stiffness |
|
| W 3/29 |
|
methods, cont.
project handouts: your project, sample rubric, project template LaTeX source (compiled PDF) |
|
| F 3/31 |
6.1, 6.2, 6.3, 6.4 |
zero-stability and convergence |
A#7 DUE |
| M 4/3 |
7.1, 7.2, 7.3, 7.4, 7.5, 7.6 |
absolute stability |
A#7 DUE |
| W 4/5 |
|
cont. |
Assignment #8 |
| F 4/7 |
|
worksheet on absolute stability: worksheet |
|
| M 4/10 |
8.1, 8.2, 8.3 |
stiffness
PROJECT V1.0 due in-class |
PROJECT V1.0 due |
| W 4/12 |
|
show and tell with PETSc |
|
| F 4/14 |
9.1, 9.2 |
heat equation (diffusion/parabolic PDEs) |
A#8 DUE
Assignment #9 |
| M 4/17 |
9.3, 9.4 |
stability of PDE schemes |
|
| W 4/19 |
10.1, 10.2 |
advection equation schemes |
|
| F 4/21 |
|
no class: SpringFest |
|
| M 4/24 |
9.5 |
convergence of PDE schemes |
A#9 DUE
CORRECTED take-home Final Exam |
| W 4/26 |
10.3, 10.4, 10.7 |
characteristics, upwind, and Lax-Wendroff
code in-class: charmovie.m |
|
| F 4/28 |
|
cont.
PROJECT V2.0 due 5pm |
PROJECT V2.0 due 5pm |
| M 5/1 |
|
cont. |
|
| F 5/5 |
|
take-home FINAL EXAM due 5pm |
FINAL EXAM due |
|