Questions about Getting Mathematica for Differential Equations

[HomogenousCow]

Hi I decided to purchase mathematica, however it appears this is a much more complicated affair than I had imagined. I will mainly be using it for differential equations (nonlinear, nonhomogenous and coupled, what have you) to help with physics. Could someone clear up some questions I have.

1.For the $295 home package do I get mathematica forever?
2.What is this kernel deal, is 4 enough for me?
3.Does mathematica require a constant internet connection for Numerical integration?
4.Is Mathematica capable of numerically solving any differential equation? (even highly nonlinear ones, like the type present in GR)

 

[leroyjenkens]

For 300$ they better have someone available to answer any question you have.

 

[Pengwuino]

Assuming you're at a university, have you checked to see if your university has a deal to provide Mathematica for their students? Mine allows you to have it for free without any license restrictions or anything.

 

[Hepth]

there's also student as long as you're a student: http://www.wolfram.com/mathematica/how-to-buy/education/students.html



1.For the $295 home package do I get mathematica forever?

Yes, but only the version you purchase, no new versions.

2.What is this kernel deal, is 4 enough for me?

1 Kernel is probably fine, 4 is enough so you can run parallel computing on 4 cores simultaneously(or have 4 independent kernels running from 4 machines connected to the one server i believe).

3.Does mathematica require a constant internet connection for Numerical integration?

No, if your license is local. (should be)

4.Is Mathematica capable of numerically solving any differential equation? (even highly nonlinear ones, like the type present in GR)

Yes it can solve many, and there are GR packages written and ready to go (for free) that set up many of these systems in a way that makes it easier for mathematica to compute.
Mathematica is also a programing language, so in addition to solving using NDSolve, you can also write the code yourself (loops/etc) to do numerical solutions if you know how.

 

[Hercuflea]

Why don't you just learn python and use Sage. Then use your school's computers for mathematica when absolutely necessary.

 

[Bill Simpson]

Hi I decided to purchase mathematica, however it appears this is a much more complicated affair than I had imagined.

Mathematica has had a reputation for being "challenging" for decades.

I will mainly be using it for differential equations (nonlinear, nonhomogenous and coupled, what have you) to help with physics. Could someone clear up some questions I have.

1.For the $295 home package do I get mathematica forever?.

Long long ago there was the student version, you get what you get, you get no support, you get no upgrades and there was the professional at 20x the price, you get support, you pay for upgrades. Since that time the number of variations has repeatedly multiplied. I think there are now student versions that last one term and that last one school year. The home version is fairly new when they realized there was a market at the price point.

Carefully read the terms of the version you are looking at and if it isn't clear then ring them on the phone and send them an email to get the details down.

There is also "Premier Support" for which you pay about that much every year. For that you can get support from them and you get upgrades.

2.What is this kernel deal, is 4 enough for me?

Back in the stone age there were even specific prices for the size of the mainframe that you wanted to run Mathematica. Individuals instead got a version that would run the graphical front end and run one background computation engine. Then with multicore processors they began selling license codes to let you run two or more computation engines.

BUT lots, probably almost all, the code inside Mathematica was written long enough ago that it is mostly all single thread single core. Just because you have four cores in your processor does not mean Mathematica suddenly starts using all four and your graphics are four times faster. Initially the only things that benefited from multiple cores was when you manually wrote code in Mathematica to hand off simple, usually numerical, calculations to a separate thread. Recently they have started adding a few more multi core functions, but still mostly it is a hold over from single core cpu days.

And to answer your question, giving away a four core license almost certainly makes no difference to you at all. It will run as fast as it runs, which is sometimes fast and sometimes not, and when it is done it is done. Because it sometimes uses symbolic functions, rather than purely FORTRAN style numeric calculations, some things can be much slower than you expect, four cores or four hundred won't help that.

3.Does mathematica require a constant internet connection for Numerical integration?

No.

4.Is Mathematica capable of numerically solving any differential equation? (even highly nonlinear ones, like the type present in GR)

Consider any other numerical differential equation library. Is that capable of solving ANY differential equation? Probably not. Did the author put in a lot of time and work specifically to solve some small subclass of the highly nonlinear ones like you want to solve? Maybe. Maybe not.

If the amount of money and particularly the amount of time you will spend trying to wrestle Mathematica to the ground and get helpful information out of it is significant then you might consider choosing a few clear specific numerical differential equations that would represent the kinds of things you need it to solve. You could then show those to the Wolfram folks and ask them whether Mathematica will breeze through those or whether it will require substantial work on your part to get dependable solutions or whether it is unlikely to ever get you a solution.

You should also probably do a book search for
Mathematica numerical differential equation
and see if you can find three or four books that have had good reviews. There are some poorly written books out there. Get your hands on the good ones and read them cover to cover. That will probably save you hundreds of hours of frustration and stomach acid.

You might also take an hour or two and compare, as much as you think you can, Mathematica against other products that would be much more narrowly focused on solving the kind of numerical differential equations that you will be working on. That might result in finding a product that could handle more of the special cases that you deal with.