The basic method for solving differential equations in a computer
is
*
finite differencing.
*
The nicest feature of the method is that it allows analysis of
objects of almost any shape, such as earth topography or geological structure.
Ordinarily, finite differencing is a straightforward task.
The main pitfall is instability.
It often happens that a seemingly reasonable approach
to a reasonable physical problem
leads to wildly oscillatory, divergent calculations.
Luckily, a few easily learned tricks go a long way,
and we will be covering them here.

- The lens equation
- First derivatives, explicit method
- First derivatives, implicit method
- Explicit heat-flow equation
- The leapfrog method
- The Crank-Nicolson method
- Solving tridiagonal simultaneous equations
- Finite-differencing in the time domain

12/26/2000