Math 615 Numerical Analysis of Differential Equations

Spring 2017, UAF

Ed Bueler:  474-7693
 elbueler@alaska.edu

Office: Chapman 301C (hours)

Class times and room:
 MWF 9:15 -- 10:15 pm
 Gruening 401

CRN:  36278

Syllabus

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