Differential Equation Graphing 439
Example Comparison of RK and Euler
Example Comparison of RK and EulerExample Comparison of RK and Euler
Example Comparison of RK and Euler
Consider a logistic growth model dP/dt = .001ùPù(100NP), 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.
12. To graph a family of solutions, return to
the Y= Editor and enter the initial
conditions shown below.
yi1={2,6,7} and yi2={5,12,18}
Note:
Use a list to specify more than one
initial condition.
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.
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