HP 50g User's Reference Manual
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Brand: HP
Category: Calculator
Type: Advanced user's reference manual
Model: HP 48gII , HP 49g+ , HP 50G
Pages: 693
Full Command and Function Reference 3-213
RRKSTEP will use the Euler method to compute the next solution step and will consider the
error tolerance satisfied. The Rosenbrock method will fail if the current independent variable is
zero and the stepsize ≤ 2.5 × 10
-499
or if the variable is nonzero and the stepsize is 2.5 × 10
-11
times its magnitude. The Runge–Kutta–Fehlberg method will fail if the current independent
variable is zero and the stepsize ≤ 1.3 × 10
-498
or if the variable is nonzero and the stepsize is 1.3
× 10
-10
times its magnitude.
Access: …µ
RRKS
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.