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There are four packages:
PARTIAL DIFFERENTIAL EQUATIONS 1
This slide show consists of graphs of numerical solutions of a particular
partial differential equation, viz. the wave equation
U + U = 0,
t x
with an initial condition of a hump resolved with 10 points. This
slide show contains: exact solution, central difference scheme,
Lax-Friedrichs scheme, upwind, Lax-Wendroff, and downwind graphs.
PARTIAL DIFFERENTIAL EQUATIONS 2
This slide show consists of graphs of numerical solutions of a particular
partial differential equation, viz. the wave equation
U + U = 0,
t x
with an initial condition of a step function. This slide show contains:
the exact solution, central difference scheme, Lax-Friedrichs scheme,
upwind, Lax-Wendroff, and downwind graphs.
PARTIAL DIFFERENTIAL EQUATIONS 3
This slide show consists of graphs of numerical solutions of a particular
partial differential equation, viz. the wave equation
U + U = 0,
t x
with an initial condition of a hump "resolved" with 1 point. This
slide contains the graphs of: the exact solution, central difference
scheme, Lax-Friedrichs scheme, upwind, Lax-Wendroff scheme, and
downwind.
VIBRATING STRING
This slide show shows how two travelling waves generate a stationary
wave.
- A. Travelling Wave
- This shows three waves simultaneously. The top one travels
to the left. The bottom one travels to the right. The middle
one is the average of the top and bottom, and is stationary.
In fact the top and bottom are the same function, viz. sin(x)
+ sin(2x), each translated by an amount ã/6 per slide, while
the domain is -4ã < x < 4ã. The stationary wave is thus the
function sin(x)cos(a) + sin(2x)cos(2a), where a is a multiple
of ã/6.
- B. Stationary Wave [0 : 2ã]
- This shows the stationary wave of (A) for 0 < x < 2ã.
- C. Stationary Wave [0 : ã]
- This shows the stationary wave of (A) for 0 < x < ã. In each
of these three cases you have the choice of stepping through
a sequence of slides one at a time, or having the computer do
it continuously and automatically (either slowly or quickly).
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Download pde1_ss.zip [101 KB].
Look at the readme file from the
program pde1_ss.zip.
Download pde2_ss.zip [84 KB].
Look at the readme file from the
program pde2_ss.zip.
Download pde3_ss.zip [92 KB].
Look at the readme file from the
program pde3_ss.zip.
Download vstri_ss.zip [94 KB].
Look at the readme file from the
program vstri_ss.zip.
Look at other programs in the University
of Arizona collection.
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