HP 50G, User Manual

Page: 409 / 887

Page 12-26
Plotting the solution to simple differential equations
The plot of a simple differential equation can be obtained by selecting
Diff
Eq
in the
TYPE
field of the PLOT SETUP environment as follows: suppose that we
want to plot x(t) from the differential equation dx/dt = exp(-t
2
), with initial
conditions: x = 0 at t = 0. The calculator allows for the plotting of the solution
of differential equations of the form Y'(T) = F(T,Y). For our case, we let Y
x
and T t, therefore, F(T,Y) f(t,x) = exp(-t
2
).
Before plotting the solution, x(t), for t = 0 to 5, delete the variables EQ and
PPAR.
Θ
Press
„ô
, simultaneously if in RPN mode, to access to the PLOT SETUP
window.
Θ
Change
TYPE
to
Diff Eq
.
Θ
Press
˜
and type
³„ ¸-~ „tQ2 @@@OK@@@
.
Θ
The cursor is now in the
H-Var
field. It should show
H-Var:0
and also
V-
Var:1
. This is the code used by the calculator to identify the variables to be
plotted.
H-Var:0
means the independent variable (to be selected later) will
be plotted in the horizontal axis. Also,
V-Var:1
means the dependent
variable (default name ‘Y’) will be plotted in the vertical axis.
Θ
Press
˜
. The cursor is now in the
Indep
field. Press
³~
„t @@@OK@@@
to change the independent variable to t .
Θ
Press
L @@@OK@@@
to return to normal calculator display.
Θ
Press
„ò
, simultaneously if in RPN mode, to access the PLOT window
(in this case it will be called PLOT WINDOW – DIFF EQ).
Θ
Change the H-VIEW and V-VIEW parameters to read:
H-VIEW: -15,V-VIEW:
-11.5
Θ
Change the
Init
value to 0, and the Final value to 5 by using:
0 @@@OK@@@
5 @@@OK@@@
.
Θ
The values Step and Tol represent the step in the independent variable and
the tolerance for convergence to be used by the numerical solution. Let’s
leave those values with their default settings (if the word
default is not
shown in the Step: field, use
L @RESET
to reset that value to its default
value. Press
L
to return to the main menu.) Press
˜
.
Θ
The Init-Soln value represents the initial value of the solution to start the
numerical result. For the present case, we have for initial conditions x(0) =
0, thus, we need to change this value to 0.0, by using
0 @@@OK@@@
.
Θ
Press
@ERASE @DRAW
to plot the solution to the differential equation.
Θ
Press
@EDIT L @LABEL @MENU
to see the graph with labels.