HP 50g User Manual Page 543

Graphing calculator.

Here we are trying to obtain the value of y(2) given y(0) = 1. With the
Soln:
field highlighted, press @SOLVE. You can check that a solution takes about
Final
6 seconds, while in the previous first-order example the solution was almost
instantaneous. Press \$ to cancel the calculation.
This is an example of a stiff ordinary differential equation.
A stiff ODE is one
whose general solution contains components that vary at widely different rates
under the same increment in the independent variable. In this particular case,
100t
the general solution, y(t) = 1+ t +C e
, contains the components 't' and
100t
'C e
', which vary at very different rates, except for the cases C=0 or C 0
100t
(e.g., for C = 1, t =0.1, C e
=22026).
The calculator's ODE numerical solver allows for the solution of stiff ODEs by
selecting the option
in the
screen. With this
_Stiff
SOLVE Y'(T) = F(T,Y)
option selected you need to provide the values of f/ y and f/ t. For the case
under consideration f/ y = -100 and f/ t = 100.
Enter those values in the corresponding fields of the
SOLVE Y'(T) = F(T,Y)
screen:
field and press @SOLVE.
When done, move the cursor to the
This
Final
Soln:
Press @EDIT to see the
time, the solution in produced in about 1 second.
solution: 2.9999999999, i.e., 3.0.
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