Re: [Phys-L] Help w/ Euler Cromer algo.

[brian whatcott <betwys1@sbcglobal.net>]

It seems to me that Fletcher illustrates the fatal flaw in proposing to 
turn students into coding aces for a research environment by using 
exercises in some programming language - a proposal that might be 
modeled as producing skilled brick-layers, when the preferred approach 
would produce architects. This was the subject of a recent thread on PHYS-L.
 In this case, Garvin & Norton use as a touchstone, a math package 
motivated by the appropriate equations.
The one they chose was MAPLE.     If students were introduced to same 
facility with MAPLE, MATHEMATICA or  MATLAB or the like,  a myriad of 
subtle errors would be avoided entirely.

Brian Whatcott

On 9/21/2014 1:47 AM, fletcher@physics.usyd.edu.au wrote:
> Hi Bernard
>
> This might help.
>
> https://www.siue.edu/~mnorton/mat-340.pdf
>
> Cheers
>
> Fletch
>
>
> Quoting Bernard Cleyet <bernard@cleyet.org>:
>
> > Cromer claim the Last Point approximation is stable.  So I must not 
> > be writing it.
> >
> >
> > My use is (to begin with) a SHM oscillator:
> >
> >
> > SUB step
> >
> > LET Q = -(g/L) * theta
> > LET thetadot = Q *deltat + thetadot
> > LET theta = theta + deltat * thetadot
> > LET t = t + deltat
> >
> > END SUB
> >
> > earlier:
> >
> > OPTION ANGLE radians
> >
> >
> > For many of my “runs” I use g = 9.8 and L to make f (of 2Pi f) one 
> > second.
> >
> >
> > Just now using one ms deltat and fitting the result to a cos; the 
> > first half second’s residuals are ~ 5e-9, doubling the second half 
> > and by the third second (cycle) the maxima are 5 e-8 (radian).
> >
> > Using a deltat of one tenth ms reduces the residuals only slightly!
> >
> > What gives?
> >
> > note:  this would be acceptable if I didn’t need to run to 100 s and 
> > longer.
> >
> > bc doesn’t want to necessarily use a fourth order approx.
> >
> >
> >
> > _______________________________________________
> > Forum for Physics Educators