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Here we are trying to obtain the value of y(2) given y(0) = 1. With the
Soln:
Final
field highlighted, press
@SOLVE
. You can check that a solution takes
about 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, the general solution, y(t) = 1+ t +C
⋅
e
100t
, contains the components ‘t’
and ‘C
⋅
e
100t
’, which vary at very different rates, except for the cases C=0 or
C
≈
0 (e.g., for C = 1, t =0.1, C
⋅
e
100t
=22026).
The calculator’s ODE numerical solver allows for the solution of stiff ODEs by
selecting the option
_Stiff
in the
SOLVE Y’(T) = F(T,Y)
screen. With this
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:
When done, move the cursor to the
Soln:
Final
field and press
@SOLVE
. This
time, the solution in produced in about 1 second. Press
@EDIT
to see the
solution: 2.9999999999, i.e., 3.0.
Note: The option
Stiff
is also available for graphical solutions of differential
equations.
Numerical solution to ODEs with the SOLVE/DIFF menu
The SOLVE soft menu is activated by using 74 MENU in RPN mode. This
menu is presented in detail in Chapter 6. One of the sub-menus, DIFF,
