Math 615 Numerical Analysis of Differential Equations

Spring 2014, Ed Bueler


Ed Bueler:  474-7693
elbueler@alaska.edu

Office
: Chapman 301C (hours)

Class times and rooms:
MWF 1:00--2:00  Reichardt 204

Required Text
:  Morton & Mayers, Numerical Solutions of Partial Differential Equations, 2nd ed., Cambridge U. Press 2005

Three other texts are recommended.  The first is freely available a page at a time, and is a great Matlab tutorial:

Syllabus

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Matlab/Octave codes:

a few Python codes:

LINKS:
Schedule:  (version 9 May, final)

Day

Section
Topic
Assigned/Due
Fri 1/17

introduction by example
MATLAB/Octave/pylab compared (PDF)
Assignment #1 (PDF)
Mon 1/20

no class: Alaska Civil Rights Day
Wed 1/22

finish example; codes
  eulerexample.m
  showlms.m
  lms.m


Fri 1/24

review of Taylor's theorem  [class cancelled]
Mon 1/27

review of Taylor's theorem A#1 DUE
Wed 1/29
2.1, 2.2
heat equation model problem A #1 DUE
Assignment #2
Fri 1/31
2.4
standard heat problem: the explicit method
from solns to A#1:
  sumthirdpower.m
  eulersoln.m
  fourierx.m
  plotfouriers.m


Mon 2/3
2.3 exact solution by Fourier series/separation of variables
Wed 2/5
2.5 standard heat problem by explicit method:  truncation error
Fri 2/7

cont.;
maximum principle proof of convergence
A #2 DUE
Assignment #3
Mon 2/10
2.6 cont., robust code, refinement paths
from solns to A#2:
  expscheme.m
  explicitfig.m
from in-class session:
 
safeexpscheme.m

Wed 2/12
2.8
implicit method
Fri 2/14

implicit method:  convergence
definitions and study guide
A #3 DUE
Assignment #4
Mon 2/17
2.7 implicit method: implementation;
Fourier/von Neumann analysis of stability
from solns to A#3:
  richardson.m
from in-class session:
  implicit.m
  implicithog.m


Wed 2/19

analysis of stability cont

Fri 2/21
2.12 cont; also Richardson method
note on stability of ODE schemes

Mon 2/24
2.10 Crank-Nicolson A#4 DUE
Wed 2/26

implement and test Crank-Nicolson
from in-class session:
   
cn.m
    cnconverge.m
A #4 DUE
Assignment #5
slides: twopoint.pdf
Fri 2/28

truncation error for theta methods

Mon 3/3
IN-CLASS MIDTERM EXAM:
closed book, no notes
covers definitions and basic calculations
Bueler in DC
Wed 3/5
no official class
online notes, for A#5:
    twopoint.pdf
    varheatSHOOT.m
    varheatFD.m
Bueler in DC
Fri 3/7
review slides; cont.
Mon 3/10
2.11
stability for theta methods A #5 DUE
Assignment #6
Wed 3/12
2.14 conservation of energy
from solns to A#5:
    exer3.m
    exer3safe.m
    exer3analysis.m
    nonlinshow.m

Fri 3/14
2.13
Neumann (flux) boundary conditions
(last day to withdraw)
from in-class session:
    neumann.m

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3/17 -- 3/21

Spring Break (no classes)
Mon 3/24
2.15
more general linear heat equation
Wed 3/26

cont.: advection and upwinding
Fri 3/28

cont.: divergence form
for A#7:
    formM.m
A #6 DUE
Assignment #7-corrected
Mon 3/31
3.1
explicit scheme for heat equation with (x,y)
from solutions to A#6:
    plotb.m
    adaptiveb.m

Wed 4/2

cont. Assignment #8
Fri 4/4

no class
INSTEAD:
   1. read 2.17 nonlinear diffusion
   2. see A#8 and these slides about ice sheet modeling

Mon 4/7
3.2
implicit schemes for 2 or 3 spatial vars
A #7 DUE
Wed 4/9
4.1
finish 2D heat stuff; see  ell.m
pure transport (=advection); characteristics
from solns to A#7:
  cnneumann.m
  meltM.m

Fri 4/11
4.2 cont.; classical wave equation;
FTCS bad, upwinding good, CFL
Version 1.0 of project DUE
project v1.0 DUE
Mon 4/14

cont.
from in-class demonstration:
   ftcs.m

Wed 4/16
4.3 convergence for upwinding Assignment #9
Fri 4/18
4.5
Lax-Friedrichs, leapfrog, and Lax-Wendroff A #8 DUE
Mon 4/21

cont.
from solns to A#8:
  barenblatt.m
  barenmovie.m
  genporouserrfig.m
  porous.m
  porousconvergefig.m


Wed 4/23
4.6, 4.9

leapfrog, shocks

Assignment #10
(CORRECTED VERSION 4)

Fri 4/25

SpringFest (no classes)
Mon 4/28

cont.

A #9 DUE
Wed 4/30 6.1
elliptic problems in 2 spatial vars
from solns to A#9:
  upwindsquare.m
  laxwendroff.m

Fri 5/2
6.2, 6.3 error analysis for elliptic;
general equilibrium diffusion

Mon 5/5
cont.
(last day of instruction; regular class day!)

Wed 5/7

ASSIGNMENT #10 (FINAL ASSIGNMENT)
DUE 5:00PM IN MY BOX (Chapman 101)

from solns to A#10:
  lfsquare.m
  maccormack.m
  leapfrog.m
  poissonrect.m
ASSIGNMENT #10 DUE
Thurs 5/8

VERSION 2.0 of PROJECT
DUE 5:00PM IN MY BOX (Chapman 101)

 
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