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The Method of Characteristics & Conservation Laws - The Shock Applet

Scott A. Sarra

Use of the applet requires the Java 1.4 browser plug-in. If this plug-in is not already installed on your computer, the web page should direct you to the site where you can freely download and install it. If the script does not direct you to the plug-in, follow this link.

The applet provides two views. The window on the left shows the initial condition advancing in time, while the window on the right shows the data advancing along the characteristics in the x-t plane.

Select one of the three example from the equations menu:

  • the advection equation,
  • the variable coefficient advection equation, or
  • inviscid Burgers' equation.

The inviscid Burgers' equation option has five submenus corresponding to five different initial conditions. Press the go button to start the animation, the stop button to stop the animation, and the reset button to return to the initial conditions. For inviscid Burgers' equation, the applet can plot the weak solution (as a solid black curve) to the problem. This option may be turned on by checking it on the options menu.

Pressing the parameters button pops up a dialog that allows five parameters to be changed by the user:

  • dX -- Controls the spacing between characteristics on the x axis.
  • dT-- Step size for time advancement. Set dT smaller to slow down the animation or to observe advancement in smaller increments along the characteristics.
  • final t -- The time at which the animation stops.
  • speed -- Animation speed. The number represents delay in milliseconds. Speed = 0 represents no delay, the fastest animation rate.
  • a - The constant advection speed in the advection equation example.

Scott A. Sarra, "The Method of Characteristics & Conservation Laws - The Shock Applet," Convergence (September 2004)


Journal of Online Mathematics and its Applications