Chapter 11: Differential Equation Graphing 193
11DIFFEQ.DOC TI-89/TI-92 Plus: Differential Equation (English) Susan Gullord Revised: 02/23/01 11:04 AM Printed: 02/23/01 2:15 PM Page 193 of 26
1. Press 3and set Graph=DIFF EQUATIONS.
2. Express the 1st-order equation
in terms of y1' and y1.
y1'=.001y1ù(100ìy1)
3. Enter the equation in the
Y= Editor ( ¥#).
4. Enter the initial condition:
yi1=10
5. Press:
ƒ 9
— or —
TI-89: ¥ Í
TI-92 Plus: ¥ F
Set Solution Method = RK and
Fields = FLDOFF.
6. In the Window Editor
( ¥$), set the
Window variables.
t0=0. xmin=ë1. ncurves=0.
tmax=100. xmax=100. diftol=.001
tstep=1. xscl=1.
tplot=0. ymin=ë10.
ymax=10.
yscl=1.
7. In the Home screen
TI-89: "
TI-92 Plus: ¥ "
use BldData to create a data
variable containing the RK
graphing points.
BldData rklog
8. Return to the Y= Editor,
press:
ƒ 9
— or —
TI-89: ¥ Í
TI-92 Plus: ¥ F
Set Solution Method = EULER.
Example Comparison of RK and Euler
Consider a logistic growth model dP/dt = .001ùPù(100ìP),
with the initial condition P(0) = 10. Use the BldData instruction
to compare the graphing points calculated by the RK and Euler
solution methods. Then plot those points along with a graph of
the equation’s exact solution.
Example
Tip: To speed up graphing
times, clear any other
equations in the Y= Editor.
With
FLDOFF
, all equations
are evaluated even if they
are not selected.
Note: You do not need to
graph the equation before
using
BldData
. For more
information about
BldData
,
refer to Appendix A.
t0 is the time at which the initial
condition occurs. By default, t0=0.
Important: Change tstep from .1
(its default) to 1. Otherwise,
BldData calculates too many
rows for the data variable and a
Dimension error occurs.
Do not use implied multiplication between
the variable and parentheses. If you do, it
is treated as a function call.