HP 48GII User Manual

Full Command and Function Reference 3-147
REWRITE
CAS: Display a menu or list of CAS operations that rewrite expressions.
RISCH
CAS: Perform symbolic integration on a function using the Risch algorithm.
RKF
Type: Command
Description: Solve for Initial Values (Runge–Kutta–Fehlberg) Command: Computes the solution to an initial
value problem for a differential equation, using the Runge-Kutta-Fehlberg (4,5) method.
RKF solves y
'(t) = f(t,y), where y(t
0
) = y
0
. The arguments and results are as follows:
• { list } contains three items in this order: the independent (t) and solution (y) variables, and
the right-hand side of the differential equation (or a variable where the expression is stored).
• x
tol
sets the absolute error tolerance. If a list is used, the first value is the absolute error
tolerance and the second value is the initial candidate step size.
• x
Tfinal
specifies the final value of the independent variable.
RKF repeatedly calls RKFSTEP as it steps from the initial value to x
Tfinal
.
Access: …µ
RKF
Input/Output:
L
3
/A
1
L
2
/A
2
L
1
/A
3
L
2
/I
1
L
1
/I
2
{ list } x
tol
x
T final
→
{ list } x
tol
{ list } { x
tol
x
hstep
} x
T final
→
{ list } x
tol
L = Level; A = Argument; I = item
See also: RKFERR, RKFSTEP, RRK, RRKSTEP, RSBERR
RKFERR
Type: Command
Description: Error Estimate for Runge–Kutta–Fehlberg Method Command: Returns the absolute error
estimate for a given step h when solving an initial value problem for a differential equation.
The arguments and results are as follows:
• { list } contains three items in this order: the independent (t) and solution (y) variables, and
the right-hand side of the differential equation (or a variable where the expression is stored).
• h is a real number that specifies the step.
• y
delta
displays the change in solution for the specified step.
• error displays the absolute error for that step. A zero error indicates that the Runge–Kutta–
Fehlberg method failed and that Euler's method was used instead.
The absolute error is the absolute value of the estimated error for a scalar problem, and the row
(infinity) norm of the estimated error vector for a vector problem. (The latter is a bound on the
maximum error of any component of the solution.)
Access: …µ
RKFE
Input/Output:
L
2
/A
1
L
1
/A
2
L
4
/I
1
L
3
/I
2
L
2
/I
3
L
1
/I
4
{ list } h
→
{ list } h y
delta
error
L = Level; A = Argument; I = item
See also: RKF, RKFSTEP, RRK, RRKSTEP, RSBERR

HP 48GII Specifications

General

Battery type	CR2032
Type	Scientific
Form factor	Pocket

Weight and Dimensions

Weight	220 g
Dimensions (WxDxH)	184 x 87 x 23.5 mm