Reference Guide

3-212 Full Command and Function Reference
The derivative of the function with respect to y (∂f/∂y) is –4y, and the derivative of the function
with respect to t (∂f/∂t) is
22
)1(
2
t
t
+
−
.
1. Store the independent variable’s initial value, 0, in T.
2. Store the dependent variable’s initial value, 0, in Y.
3. Store the expression,
2
2
2
1
1
y
t
−
+
, in F.
4. Store ∂f/∂y, –4y, in FY.
5. Store ∂f/∂t,
22
)1(
2
t
t
+
−
, in FT.
6. Enter these five items in a list: { T Y F FY FT } .
7. Enter the tolerance. Use estimated decimal place accuracy as a guideline for choosing a
tolerance: 0.00001.
8. Enter the final value for the independent variable: 8.
The stack should look like this:
{ T Y F FY FT }
.00001
8
9. Press RRK . The variable T now contains 8, and Y now contains the value .123077277659.
The actual answer is .123076923077, so the calculated answer has an error of approximately
.00000035, well within the specified tolerance.
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