HP 48GII

Full Command and Function Reference 3-155
Input/Output:
L
4
/A
1
L
3
/A
2
L
2
/A
3
L
1
/A
4
L
4
/I
1
L
3
/I
2
L
2
/I
3
L
1
/I
4
{ list } x
tol
h last
→
{ list } x
tol
h
next
current
L = Level; A = Argument; I = item
See also: RKF, RKFERR, RKFSTEP, RRK, RSBERR
RSBERR
Type: Command
Description: Error Estimate for Rosenbrock Method Command: Returns an error estimate for a given step h
when solving an initial values problem for a differential equation.
The arguments and results are as follows:
• { list } contains five items in this order:
– The independent variable (t).
– The solution variable (y).
– The right-hand side of the differential equation (or a variable where the expression is
stored).
– The partial derivative of y'(t) with respect to the solution variable (or a variable where the
expression is stored).
– The partial derivative of y'(t) with respect to the independent variable (or a variable where
the expression is stored).
• h is a real number that specifies the initial step.
• y
delta
displays the change in solution.
• error displays the absolute error for that step. 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.) A zero error indicates that the Rosenbrock method failed and Euler
's method was
used instead.
Access: …µ
RSBER
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, RKFERR, RKFSTEP, RRK, RRKSTEP
RSD
Type: Command
Description: Residual Command: Computes the residual B – AZ of the arrays B, A, and Z.
A, B, and Z are restricted as follows:
• A must be a matrix.
• The number of columns of A must equal the number of elements of Z if Z is a vector, or the
number of rows of Z if Z is a matrix.
• The number of rows of A must equal the number of elements of B if B is a vector, or the
number of rows of B if B is a matrix.
• B and Z must both be vectors or both be matrices.
• B and Z must have the same number of columns if they are matrices.
RSD is typically used for computing a correction to Z, where Z has been obtained as an
approximation to the solution X to the system of equations AX = B.
Access: !Ø
OPERATIONS LRSD ( Ø is the left-shift of the 5key).
!´
MATRIX LRSD ( ´ is the left-shift of the Pkey).