Diffeq - HP 48gII Advanced User's Reference Manual

Graphing calculator
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DIFFEQ

Type:
Command
Description: Differential Equation Plot Type Command: Sets the plot type to DIFFEQ.
When the plot type is DIFFEQ and the reserved variable EQ does not contain a list, the initial
value problem is solved and plotted over an interval using the Runge–Kutta–Fehlberg (4,5)
method. The plotting parameters are specified in the reserved variable PPAR, which has the
following form:
For plot type DIFFEQ, the elements of PPAR are used as follows:
(xmin, ymin) is a complex number specifying the lower left corner of PICT (the lower left
corner of the display range). The default value is (–6.5,–3.1) for the hp48gII and (–6.5,–3.9)
for the hp49g+.
(xmax, ymax) is a complex number specifying the upper right corner of PICT (the upper
right corner of the display range). The default value is (6.5,3.2) for the hp48gII and (6.5,4.0)
for the hp49g+.
indep is a list, { X x
numbers that specify the initial and final values for the independent variable. The default
values for these elements are { X 0 xmax }.
res is a real number specifying the maximum interval, in user-unit coordinates, between
values of the independent variable. The default value is 0. If res does not equal zero, then the
maximum interval is res. If res equals zero, the maximum interval is unlimited.
axes is a list containing one or more of the following, in the order listed: a complex number
specifying the user-unit coordinates of the plot origin, a list specifying the tick-mark
annotation, and two strings specifying labels for the horizontal and vertical axes. If the
solution is real-valued, these strings can specify the dependent or the independent variable; if
the solution is vector valued, the strings can specify a solution component:
– 0 specifies the dependent variable (X)
– 1 specifies the dependent variable (Y)
– n specifies a solution component Y
– If axes contains any strings other than 0, 1 or n, the DIFFEQ plotter uses the default
strings 0 and 1, and plots the independent variable on the horizontal axis and the
dependent variable on the vertical.
ptype is a command name specifying the plot type. Executing the command DIFFEQ places
the command name DIFFEQ in PPAR.
depend is a list, { Y y
solution), and two numbers that specify the initial value of Y and the global absolute error
tolerance in the solution Y. The default values for these elements are { Y 0 .0001 }
EQ must define the right-hand side of the initial value problem Y'(XF(X,Y). Y can return a real
value or real vector when evaluated.
The DIFFEQ-plotter attempts to make the interval between values of the independent variable
as large as possible, while keeping the computed solution within the specified error tolerance
x
. This tolerance may hold only at the computed points. Straight lines are drawn between
ErrTol
computed step endpoints, and these lines may not accurately represent the actual shape of the
solution. res limits the maximum interval size to provide higher plot resolution.
On exit from DIFFEQ plot, the first elements of indep and depnd (identifiers) contain the final
values of X and Y, respectively.
3-46 Full Command and Function Reference
{ (x
) (x
) indep res axes ptype depend }
, y
, y
min
min
max
max
x
}, containing a name that specifies the independent variable, and two
0
f
n
x
}, containing a name that specifies the dependent variable (the
0
ErrTol

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