Example Comparison Of Rk And Euler - Texas Instruments TI-89 Manual Book

Example Comparison of RK and Euler

Example
Tip: To speed up graphing
times, clear any other
equations in the Y= Editor.
With , all equations
FLDOFF
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.
Consider a logistic growth model dP/dt = .001ù Pù (100ì 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.
1. Press 3 and set
2. Express the 1st-order equation
in terms of and
y1'
Do not use implied multiplication between
the variable and parentheses. If you do, it
3. Enter the equation in the
Y= Editor ( ¥ # ).
4. Enter the initial condition:
yi1=10
5. Press:
ƒ
9
— or —
¥ Í
TI-89:
¥
TI-92 Plus: F
Set
Solution Method = RK
.
Fields = FLDOFF
6. In the Window Editor
( ¥ $ ), set the
Window variables.
7. In the Home screen
: "
TI-89
TI-92 Plus: ¥ "
use BldData to create a data
variable containing the
graphing points.
8. Return to the Y= Editor,
press:
ƒ
9
— or —
¥ Í
TI-89:
¥
TI-92 Plus: F
Set
Solution Method = EULER
Chapter 11: Differential Equation Graphing
Graph=DIFF EQUATIONS
.
y1
is treated as a function call.
t0 is the time at which the initial
condition occurs. By default, t0=0.
and
t0=0.
tmax=100.
tstep=1.
tplot=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.
BldData rklog
RK
.
.
y1'=.001y1ù (100ì y1)
xmin=ë 1. ncurves=0.
xmax=100. diftol=.001
xscl=1.
ymin=ë 10.
ymax=10.
yscl=1.
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