Example comparison of rk and euler – Texas Instruments TITANIUM TI-89 User Manual
Page 439

Differential Equation Graphing
439
Example Comparison of RK and Euler
Example Comparison of RK and Euler
Example Comparison of RK and Euler
Example Comparison of RK and Euler
Consider a logistic growth model
dP/dt = .001
ù
P
ù
(100
N
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
Example
Example
Example
13. Return to the Graph screen, which
displays a curve for each pair of initial
conditions.
14. Press
… to trace. Then press
3
¸ to
see the number of foxes (
xc
) and rabbits
(
yc
) at
t=3
.
Because
t0=0
and
tmax=10
, you can trace
in the range 0 t 10.
Note:
Use
C and D to move the trace
cursor from one initial condition curve to
another.
1. Press
3 and set
Graph=DIFF
EQUATIONS
.