Texas Instruments PLUS TI-89 - Manual (Page 210)

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 3 and set Graph=DIFF EQUATIONS .
2. Express the 1st-order equation
in terms of y1' and y1 .
y1'=.001y1 щ (100 м y1)
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= ë 1. ncurves=0.
tmax=100. xmax=100. diftol=.001
tstep=1. xscl=1.
tplot=0. ymin= ë 10.
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 = .001 ù P щ (100 м P),
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.