How does the computer model differential equations ?
We know from calculus that on a graph of Y versus X the derivative
dY/dX at any point of the curve is equal to the slope. We can take
the differential equation for the curve and substitute in numbers
to calculate the slope at a given point. By casting this slope
through this point in the direction of the next point, we can project
and estimate its value. This is shown on the sketch. Given some
Point #1, we substitute into the dY/dX equation to get the slope
and project to Point #2. We again substitute into the equation to
get the slope at this point and project to Point #3. This is shown
with blue construction lines on this sketch up to Point #4, and
the yellow line represents extending the process.
while on sabbatical leave as ESB, Porto, Portugal, 1996