Rsberr; Rsd - HP 48gII Advanced User's Reference Manual

Input/Output:
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 displays the change in solution.
delta
• 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.
...µ
Access:
Input/Output:
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.
!Ø
Access:
!´
L /A L /A
4 1 3 2
{ list } x
tol
L = Level; A = Argument; I = item
RSBER
L /A L /A
2 1 1 2
{ list } h
L = Level; A = Argument; I = item
L
OPERATIONS RSD
L
MATRIX RSD
L /A L /A
2 3 1 4
h last { list }
L /I
4 1
{ list }
( Ø is the left-shift of the 5key).
( ´ is the left-shift of the Pkey).
Full Command and Function Reference 3-155
L /I L /I L /I
4 1 3 2 2 3
x h
tol next
L /I L /I
3 2 2 3
h y
delta
L /I
1 4
current
L /I
1 4
error