PARTIAL DIFFERENTIAL EQUATIONS SLIDE SHOWS

Department of Mathematics
University of Arizona
Tucson, Arizona 85721

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).

Look at the readme file from the program pde1_ss.zip.