Solutions to complex differential
equations are easy to plot accurately because interpolating
functions are used to represent them.
Mathematica is unique in returning the results of numerical
superfunctions (e.g.NDSolve)
as symbolic functions representing the interpolation through
ordinates taken--the interpolating object. This is in contrast to
purely numerical systems, which return an unprocessed list of numbers.
Interpolating objects make results easily and immediately usable:
for example, plotting, differentiating, or finding a specific value
(whether or not it was picked for evaluation during the computation)
can all be performed with a result as if it were any built-in
mathematical function.