Splash

This page shows a splash in a pond. The animations produced by DPGraph and Mathematica are compared.

A solution to the wave equation, u_tt = u_xx + u_yy, which is periodic in time, radially symmetric, and has outgoing waves is

u =J₀(r)cos(t) + Y₀(r)sin(t) , where J₀ and Y₀ the Bessel functions of the first and second kind (both of order 0). The second function, Y₀, is unbounded as r approaches 0.

The Bessel functions are defined in Mathematica, but not in DPGraph, where I used approximations involving sines and cosines.

Click on the thumbnail to run the animation. To stop the DPGraph animation, close the program. To stop the Mathematica animation, which is an animated GIF displayed by your browser, click "back."

DPGraph (654 Bytes, < 1 KB)
Mathematica (594 KB)
The Mathematica source code that produced the animated GIF is here (6 KB). You may download it and use it as a template for your own animations.

Jim Swift's DPGraph page Jim Swift's home page Department of Mathematics NAU
e-mail: Jim.Swift@nau.edu