Is there a program to solve any equations?

[olgerm]

Is there any program that could find approximate solutions to any equations system? For example to N-body problem (equations)? Could it also find a function from differential equations like N-body problem ones?
If so ,then why are N-body simulators needed?

 

[SteamKing]

Is there any program that could find approximate solutions to any equations system? For example to N-body problem (equations)? Could it also find a function from differential equations like N-body problem ones?
If so ,then why are N-body simulators needed?

Because no one has found any mathematical function or combination of functions which solve the general N-body problem. Even the familiar 2-body problem can be solved only by neglecting the influence of every other mass in the universe.

In order to proceed with any type of analysis, for now, this must be done using numerical simulations. Certain questions remain unresolved, even using this technique. For example, over the long term, are the orbits of the planets in the solar system stable, or will there come a time when one or more planets will be ejected into interstellar space?

Even solving systems of elementary differential equations is fraught sometimes with difficulty. The final results are often highly dependent on the accuracy of the initial conditions input to solve the problem. The investigation of how the approximate solutions to such equations has led to new areas of mathematical study like chaos theory:

https://en.wikipedia.org/wiki/Chaos_theory

 

[jedishrfu]

Cornell Univ researchers developed a program a few years ago that could generate a formula given the data. It was used successfully to determine the equation for a compound pendulum.

Some biology researchers used it to determine a formula for some cellular mechanism they were studying. They were ecstatic when it discovered the equation but then depressed when they couldn't explain the terms in it. So while it worked, the equation was useless for publication if you can't develop a theory to base the equation on.

From WIRED:

http://www.wired.com/2009/04/Newtonai/

and Cornell in more detail.

http://creativemachines.cornell.edu/natural_laws

and Cornell in less detail:

http://www.news.cornell.edu/stories/2009/04/computer-derives-natural-laws-observation

 

[olgerm]

Because no one has found any mathematical function or combination of functions which solve the general N-body problem.

I know that ,but I was asking about program, that could find approximate solutions for any equations system.

In order to proceed with any type of analysis, for now, this must be done using numerical simulations.

Do you know which programs are being used for simulations? Are these programs N-body simulators or programs ,which can simulate any equation?

 

[jedishrfu]

I'm sure there are many custom programs written in MATLAB or Mathematica that handle these kinds of problems if you search for them

You could also check the Open Source Physics site (http://www.opensourcephysics.org/) for java-based N-body programs. I do know they have a 3-body version with the three well known exact solutions:

Look for the PlanarNBodyApp.java and PlanarNBody.java (Open Source Physics Guide Chapter 9)

You can download the workspace_compadre.zip and use the Eclipse or Netbeans IDE to import it and run it.

or you write your own using Processing IDE (processing.org) or any other system with graphical capabilities.

What is your interest in this problem?

 

[olgerm]

What is your interest in this problem?

I have programmed a simple N-body simulator. Now i have started thinking ,that I could have just wrote a script ,that forms N-body problem equations by user input and uses some software to find approximate solutions to these equations.
Is there any point at all in using N-body simulator if exist an universal program ,which can to find approximate solutions to any equations system (including N-body problem equation system)?

 

[SteamKing]

I have programmed a simple N-body simulator. Now i have started thinking ,that I could have just wrote a script ,that forms N-body problem equations by user input and uses some software to find approximate solutions to these equations.
Is there any point at all in using N-body simulator if exist an universal program ,which can to find approximate solutions to any equations system (including N-body problem equation system)?

There are no "universal" solution programs. I'm not sure how any such software could even be developed.

There are a number of different programs which can solve a large subset of related problems, but only because the underlying mathematics is the same or very similar.

One such type of program uses the finite element method, which can be applied to solve problems in analyzing complex structures, acoustics, hydrodynamics, and several other different areas.

 

[Hornbein]

Cornell Univ researchers developed a program a few years ago that could generate a formula given the data. It was used successfully to determine the equation for a compound pendulum.

Some biology researchers used it to determine a formula for some cellular mechanism they were studying. They were ecstatic when it discovered the equation but then depressed when they couldn't explain the terms in it. So while it worked, the equation was useless for publication if you can't develop a theory to base the equation on.

The formula was probably some senseless thing produced via "overfitting" that would work only in that exact circumstance. Expect to see a lot of that in the future: misapplications of "deep learning." What we will get are complex, inexplicable cybersuperstitions. No stopping it.

 

[FactChecker]

When you ask about "approximate" solutions, @SteamKing 's comment about Chaos Theory is important to note. If 2 planets pass close to each other, the direction they go can depend completely on how they pass each other. So an approximate answer can be very sensitive to exact calculations that can not be "approximate" at all.