Greetings all, While a grad student at Illinois, I took a course on numerical methods that was taught out of a textbook by a professor at Illinois: http://www.amazon.com/Scientific-Computing-Michael-T-Heath/dp/0072399104
I found the book to be well written and quite readable. Furthermore, all algorithms were notated as algorithms: there was no code written in any particular language, which I liked a lot. This gave me the enjoyable mental challenge of implementing the algorithm in my chosen language (PDL), and avoided issues such as Numerical Recipes' copyright/license restrictions. David On Tue, Dec 30, 2014 at 1:03 AM, Craig DeForest <defor...@boulder.swri.edu> wrote: > The rabbit hole (of computational simulation of multivariate differential > equations) goes very deep. Koonin's "Computational Physics" is a good > place to start, along with (of course) Numerical Recipes. > > Note that your formula for Acceleration is incorrect - the "/" has higher > precedence than "+" or "-", so you will not get the ratios that you think > you are. > > It is better, when discretizing differential equations, to use a separate > variable to hold the discrete differentials - that way you can change the > differential approximation you use, without having to overhaul the main > formula. You can pick and choose your discrete approximation to get faster > convergence to the true differentials - for example, a popular one is RK4, > a method that is slightly more involved than the simple first-order > discrete difference you used - but converges like (delta_t)^4 instead of > just (delta_t). What methods you use will depend on how large your problem > is, how many times you want to solve it, and how accurate you need your > answer to be. Almost any introductory text on numerical methods will > discuss these things. Koonin is over 20 years old now, and Numerical > Recipes is even older - but the basics remain the same although the > computers have gotten about 10,000 times faster. > > Sent from my ipad - sorry for any typos > > On Dec 29, 2014, at 7:32 PM, Mark Baker <mrbaker_...@yahoo.com> wrote: > > Hello > > I was Wondering if anyone knows of a good Multivariable Calculus book to > use with PDL > I have a few yet they seem more geared toward Mathematica . > > I'm having a problem trying to deduce the mass formula in PDL, and I > wonder if the > PDL frame work in TriD was made to do this easily like Energy= x*y*z or > Mass = x*y*z > > I do make some attempts at finding this yet I find that I need to prove > these formulas > http://www.nanonebula.com/electron_refined.txt > > I found that for the acceleration the formula is > $Acceleration = sum( sqrt( ($x2 - $x1 / $t2 - $t1)**2 + ($y2 - $y1 / $t2 > - $t1)**2 + ($z2 -$z1 / $t2 - $t1)**2) ); > where $t = time > I can prove this by using this logic here > $Radius = ($x**2 + $y**2 +$z**2 ) > $Length = sum(2*$radius); > $time = sqrt($Length / $Acceleration ) > and if time is right then I know this formula is right > > > I see in the text book it says to use a triple integral over the > Density*Volume > Is there a special formula for finding the mass of a particle system in > PDL ??? > > so Is sum($x + $y + $z ) the same as a triple integral for x y z ??? > > Best Regards, > > -Mark > > <http://www.nanonebula.com/electron_refined.txt> > > _______________________________________________ > Perldl mailing list > Perldl@jach.hawaii.edu > http://mailman.jach.hawaii.edu/mailman/listinfo/perldl > > > _______________________________________________ > Perldl mailing list > Perldl@jach.hawaii.edu > http://mailman.jach.hawaii.edu/mailman/listinfo/perldl > > -- "Debugging is twice as hard as writing the code in the first place. Therefore, if you write the code as cleverly as possible, you are, by definition, not smart enough to debug it." -- Brian Kernighan
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