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Function RRKSTEP
This function uses an input list similar to that of function RRK, as well as the
tolerance for the solution, a possible step
∆
x, and a number (LAST) specifying
the last method used in the solution (1, if RKF was used, or 2, if RRK was
used). Function RRKSTEP returns the same input list, followed by the tolerance,
an estimate of the next step in the independent variable, and the current
method (CURRENT) used to arrive at the next step. Thus, the input stack looks
as follows:
4: {‘x’, ‘y’, ‘f(x,y)’}
3:
ε
2:
∆
x
1: LAST
After running this function, the stack will show the lines:
4: {‘x’, ‘y’, ‘f(x,y)’}
3:
ε
2: (
∆
x)
next
1: CURRENT
Thus, this function is used to determine the appropriate size of a time step
((
∆
x)
next
) to satisfy the required tolerance, and the method used to arrive at that
result (CURRENT).
The following screen shots show the RPN stack before and after application of
function RRKSTEP:
These results indicate that (
∆
x)
next
= 0.00558… and that the RKF method
(CURRENT = 1) should be used.