Rewrite; Risch; Rkf; Rkferr - HP 48gII Advanced User's Reference Manual

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
• { 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 sets the absolute error tolerance. If a list is used, the first value is the absolute error
tol
tolerance and the second value is the initial candidate step size.
• x specifies the final value of the independent variable.
Tfinal
RKF repeatedly calls RKFSTEP as it steps from the initial value to x
...µ
Access:
Input/Output:
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 displays the change in solution for the specified step.
delta
• 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.)
...µ
Access:
Input/Output:
See also: RKF, RKFSTEP, RRK, RRKSTEP, RSBERR
0
RKF
L /A L /A
3 1 2
{ list } x
tol
{ list } { x x
tol
L = Level; A = Argument; I = item
RKFE
L /A L /A
2 1 1 2
{ list } h
L = Level; A = Argument; I = item
) = y . The arguments and results are as follows:
0
L /A
2 1 3
x
T final
} x
hstep T final
L /I
4 1
{ list }
Full Command and Function Reference 3-147
.
Tfinal
L /I
2 1
{ list }
{ list }
L /I L /I
3 2 2 3
h y
delta
L /I
1 2
x
tol
x
tol
L /I
1 4
error