3-154 Full Command and Function Reference
–
The partial derivative of y'(t) with respect to the independent variable (or a variable where
the expression is stored).
• x
tol
sets the tolerance value. If a list is used, the first value is the tolerance and the second
value is the initial candidate step size.
• x
Tfinal
specifies the final value of the independent variable.
RRK repeatedly calls RKFSTEP as its steps from the initial value to x
Tfinal
.
Access: …µ
RRK
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: RKF, RKFERR, RKFSTEP, RRKSTEP, RSBERR
RRKSTEP
Type: Command
Description: Next Solution Step and Method (RKF or RRK) Command: Computes the next solution step
(h
next
) to an initial value problem for a differential equation, and displays the method used to
arrive at that result.
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).
• x
tol
is the tolerance value.
• h specifies the initial candidate step.
• last specifies the last method used (RKF = 1, RRK = 2). If this is the first time you are using
RRKSTEP, enter 0.
• current displays the current method used to arrive at the next step.
• h
next
is the next candidate step.
The independent and solution variables must have values stored in them. RRKSTEP steps these
variables to the next point upon completion.
Note that the actual step used by RRKSTEP will be less than the input value h if the global error
tolerance is not satisfied by that value. If a stringent global error tolerance forces RRKSTEP to
reduce its stepsize to the point that the Runge–Kutta–Fehlberg or Rosenbrock methods fails,
then 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
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