Code: drop1.m.

Animation: drop_movie.gif (warning: 4.8MiB gif). Also, my apologies for the colors, I should read up on caxis for how to add some meaningful color information that is not autoscaled at each time step.

Script to make gif: make_movie.sh

photos of board: on Ben's seminar page.

codes: iter_driver.m, iter_f_lam.m, and iter_f_psi.m.

In the following pictures, the initial conditions are the same (k=2,l=2) except for the amplitude with epsilon=1/16 and lambda0=-19.7392

lambda: -19.773

initial amplitude=1

N=16

lambda: -33.057

initial amplitude=20

N=16

lambda: -73.01

initial amplitude=40

N=20

lambda: -207.02

initial amplitude=75

N=36

lambda: -209.53

initial amplitude=75.5

N=36

lambda: -212.05

initial amplitude=76

N=36

lambda: -217.14

initial amplitude=77

N=36

The following animation shows the evolution of an initial Gaussian pulse under zero potential:

Here is a MNG animation of the same thing if your browser supports it.

- schrod1.mws (maple 7)
- schrod1.mw (maple 9)

- Make the animation in maple (see the worksheets above for how to do this)
- Right-click on the animation, selected export-as->GIF
- Use the unix command
`convert`

(part of the ImageMagick package like this:

`convert test.gif test-c.gif`

This will half the size of your animation. You may need recent ImageMagick, possibly one released after 2003-06-20 when the LZW patent expired in the USA. Note this patent is still valid in Canada,**use gifs at your own risk**. - You can also make a MNG like this:

`convert test.gif test-c.mng`

but browser support for .mng seems minimal without a plugin.

Follow this link for photographs of the blackboards.

Philip’s codes:
`wave1.m`

,
`wave1_f.m`

,
`wave1.m`

,
`wave1_f.m`

, and
`convtest.m`

.

Follow this link for photographs of the blackboards.

Solving backwards numerically starting in the right-hand singular point, we compute the value of η such that w(η)=0. Example outputs from the code for three difference tolerances are:

This process seems sensitive to the tolerances specified to `ode15s`

; the following plot shows the stopping value against the relative tolerance (red circles show solutions which diverged and never reached zero):

Clearly, we cannot trust this code to capture the correct solution as it passes through the middle singular point. *Also, if you look very closely at the last plot, it actually resembles a batch of chocolate chip cookies.*

The codes can be downloaded here:
`driver3.m`

,
`odef3_rhs.m`

,
`odef3_mass.m`

, and
`odef3_events.m`

.

My earlier code also has trouble crossing the middle singular from the left-hand side. See plots of the 2nd derivative and the 3rd derivative.

Download a `maple`

code `subs_first_terms.mw`

to sub in the first two terms of the w1 solution at the middle singular point.

Follow this link for photographs of the blackboards.

My first code (*seems* to integrate across middle singularity): driver1.m, odef1_rhs.m, odef1_mass.m, odef1_jac.m.

The code we wrote during the Thursday session (starts in the right-hand singularity and integrates forward and backward): driver2.m, odef2_rhs.m.

Photographs of the board:

- Side boards:
- The front board:

Photographs of the board from Thursday afternoon:

- Given equations and steady solution, find disturbance equations and nondimensionalization (n19n):
- 20040205-board06.jpg (dropping nonlinear terms)
- 20040205-board07.jpg
- 20040205-board08.jpg (DAEs)
- 20040205-board09.jpg
- 20040205-board10.jpg
- 20040205-board11.jpg (a second order ODE!):

- A Maple7 worksheet for the DAE calculations: DAEs.mws.
- Photo of Dave, Ben and Colin.

Photograph of the board from the Thursday session (first-order corrections for L1, L2):

Friday afternoon (leading order and first-order corrections for L3, L4, and L5:

Photographs of the board:

Based on cbm’s codes from last week.

`vdp_period2.m`

, an updated version of last weeks code, still uses the helper functions from last week, vdp_period_f.m and vdp_period_events.m.- Computes the first airy root:
`vdp_first_airy_root.m`

. - The processing code:
`vdp_period_plot2.m`

. This code calls`vdp_first_airy_root.m`

. `vdp_period2.m`

takes a long time to run. The`.mat`

data file it creates is`vdp_period_datafile2.mat`

. I suspect this file is not architecture/matlab version independent but its worth a shot.

MathML test: $x\text{'}\text{'}+\mu ({x}^{2}-1)x\text{'}+x$.

This code computes solutions to the van der Pol oscillator and displays them in the phase plane.

For various values of mu, this code numerically estimates the period of the van der Pol oscillator. The results are compared with the leading order analytic results and the second order correction is estimated.

- The period computing code: vdp_period.m
- Two helper functions: vdp_period_f.m and vdp_period_events.m
- The processing code: vdp_period_plot.m

Various photographs of the board:

- sem20031017_board1.jpg
- sem20031017_board2.jpg
- sem20031017_board3.jpg
- sem20031017_board4.jpg
- sem20031017_board5.jpg

Various material on this page may be copyright of the original authors.
Contact david.murak[at]sfu.ca for more information.

This webpage itself is copyright © 2004 Colin Macdonald.

Verbatim copying and distribution of parts © Colin Macdonald
is permitted in any medium, provided this notice is preserved.