dextercioby said:Using calculators...?The equations in physics are usually nonintegrable analytically,many of them are quasi/nonlinear (starting with Newton's gravity law,for example) and therefore the dynamics is found either intuitively or using a computer...
There are fortunate exceptions...The Schwarzschild solution is one of them.
Daniel.
Starship said:How do professional scientists make sophisticated calculations, e.g the http://arxiv.org/PS_cache/math-ph/pdf/0412/0412064.pdf in general relativity? Are there any special algorithms for this?
I'd really like to solve these equations but it's almost impossible without computer help.
robphy said:The symbolic tensorial and spinorial calculations in the paper above are probably done by hand.
One can use tools like GRTensor and others to symbolically verify some calculations or evaluate tensor components [given component functions of the metric, for example].
To go beyond symbolic calculations, you'll need to find or write specialized software to solve systems of nonlinear PDEs. For these, you might start here
http://jean-luc.aei.mpg.de/
http://numrel.aei.mpg.de/
http://bh0.physics.ubc.ca/People/matt/555/
and the Numerical Relativity articles at
http://relativity.livingreviews.org/Articles/subject.html
Sophisticated calculations refer to complex mathematical and statistical algorithms that are used to solve problems or make predictions in various fields such as physics, chemistry, engineering, and finance.
Sophisticated calculations involve advanced programming techniques and complex mathematical models, while regular calculations are simple arithmetic operations. Sophisticated calculations also require specialized software and powerful computing resources.
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The accuracy of sophisticated calculations depends on the quality of the data input and the complexity of the mathematical model used. In general, these calculations can provide highly accurate results, but there is always a margin of error that needs to be considered.
Sophisticated calculations require a strong background in mathematics and programming. While anyone can learn these skills, it takes years of study and practice to become proficient in performing sophisticated calculations. Additionally, access to specialized software and computing resources is often necessary.