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Mathematica 3 vs. Mathematica 13: solving complex differential equations

Posted 1 year ago

I have a number of Mathematica notebooks using complex differential equations from when I was using Mathematica 3. My concern is that with a current good computer it is taking about the same amount of time to run my notebooks in Mathematica 13 as it did in Mathematica 3 twenty years ago. The memory usage has increased from a few hundred MB to thirteen GB. Has anyone experienced anything similar? Any explanations?

I have included a Mathematica notebook and package. Both contain documentation but the application is based on the evaluation of combinatorial enumerated structures and is difficult to follow without understanding both dynamics and combinatorics.

Edit: Stephen Wolfram suggested I submit my work to Wolfram Functions on extending tetration to the complex numbers and the same for the Ackermann function. This code forms the foundation for extending tetration.

POSTED BY: Daniel Geisler
3 Replies

After reviewing the compile tutorial I believe I can migrate my code to a compiled version that is radically faster than anything earlier versions of Mathematica's could perform.

POSTED BY: Daniel Geisler

I should have explained that I had the value of size=5 in Iterate[f,n,z,p,size] so that the program would execute in an acceptable time. The fifth derivate is comprised of 236 components while the eight derivate, size=8, has 660,032 components where the evaluation of the components contains an exponentially growing number of terms. I have a good computer yet the program ran for many hours with eight derivates. It had consumed almost all available RAM which slowed the program down.

Is there any resources for what can compile? Should I study LLVM? Or do I need to experiment a great deal?

POSTED BY: Daniel Geisler

Very hard to say without having both systems and so on. Likely functionality has been added that would solve the problem in a much more efficient manner using built-in functions. It could even be that some wrappers you used before are now actually evaluated, causing it to be more time. really hard to say basically. Most of the code in the notebook runs instantaneously for me, so hard to time as well…

POSTED BY: Sander Huisman
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