(48G 49G 50G) Runge-Kutta Diff Eqn solver

[rcthacker]

Again, thank you, Werner, for your enlightening comments and discussion.

I went through my copy of Bill Wickes' HP-28 Insights looking for Expressions, Equations, Programs, and their equivalence. Probably the best description is on page 90, 6.3 Symbolic Math (First Edition, First Printing):

"As we will show in section 9.1, algebraic objects are procedures that are internally the same as programs. So just creating any algebraic object is equivalent to writing a program. Its "inputs" are the values stored in the variables named within the algebraic object; its "output" is the symbolic or numeric result that is returned to the stack. . . "

I couldn't find a copy of his HP-48 Insights, but I imagine it would say the same. In section 9.1 he does say, in effect, that algebraics are more restrictive.

"All equations have program equivalents, but not all programs can be turned into equations, so I would have been very surprised if the input had been limited to equations only." I doubt the firmware writers designed the input arguments to allow for this. Sort of like an unsupported feature. But, maybe it is a central if undescribed characteristic of the RPL design.

Since I was unable to access the necessary variable in my original attempt to solve the 2nd order DE, it was very valuable that you showed how an RPN procedure could provide the required "inputs" and return the required "outputs". All the examples in the 48G and 50G Guides and AURs (nothing for the 49G) show only algebraics or a matrix-vector product - no RPN procedures. The problem could only be solved using RPN commands not allowed in an algebraic object. In a straight-forward Runge-Kutta code all of the function inputs and outputs would be accessible variables. It's a mystery to me that the firmware writers decided to represent 2nd order DEs with a matrix of coefficients and a vector of dependent variables: neither representable in an algebraic expression/object in the RPL OS/User language. Maybe an academic feature.