Numerical Solutions

Numerical Solutions refers to a response to the Three Body Problem which claims that there are working celestial models with three or more bodies. It is suggested by some sources that numerical solutions exist which can simulate the n-body systems proposed by conventional astronomy. However, it is seen that 'numerical solutions' refers to methods of approximations. The solutions for n-body problems where N > 2 do not fully simulate gravity and involve liberal assumptions.

N-Body Quotes
From p.89 of Atmospheric and Space Flight Dynamics: Modeling and Simulation with MATLAB (Archive) by Professor Ashish Tewari (bio) we read:



On p.2 of a Master's thesis Evaluation of mass loss in the simulation of stellar clusters using a new multiphysics software environment (Archive) by Guillermo Kardolus we see:





A Princeton University programming assignment (Archive) says:



The paper Global Error Measures for Large N-Body Simulations (Archive.is) describes:



General Quotes
The book Nuclear Astrophysics: A Course of Lectures tells us on p.259:



The abstract of a medical research paper Simulation and air-conditioning in the nose (Archive) says:



From a question posted on researchgate.net (Archive):




 * Mohammad Firoz Khan, Ph.D. responds:



Jason Brownlee, Ph.D., tells us on machinelearningmastery.com (Archive):



http://www.math.pitt.edu/~sussmanm/2071Spring09/lab02/index.html (Archive)



Two Body Approximations
https://www.askamathematician.com/2011/10/q-what-is-the-three-body-problem/ (Archive)



https://academic.oup.com/mnras/article/440/1/719/1747624 (Archive)



https://hanspeterschaub.info/Papers/UnderGradStudents/ConicReport.pdf (Archive)



https://academic.oup.com/mnras/article/452/2/1934/1069988 (Archive)



On particle physics - https://academic.oup.com/mnras/article/440/1/719/1747624 (Archive)



Four Body Approximation
http://www.cds.caltech.edu/~marsden/volume/missiondesign/KoLoMaRo_DMissionBook_2011-04-25.pdf (Archive)

5.3 Bicircular Model 126 5. Trajectories in the Four-Body Problem



Galaxy Simulator
The following was provided to us as an example of the numerical solution of multiple bodies - The Numerical Solution of the N-Body Problem (Archive). Read the below quotes and decide whether the methods are describing a full simulation of gravity.

From the introduction of the paper:



Looking up 'Barnes Hut' we find: https://beltoforion.de/en/barnes-hut-galaxy-simulator/ (Archive)


 * The Barnes-Hut Galaxy Simulator



The above shows that there could be a numerical solution that doesn't use gravity fully, discrediting the "numerical solutions exist" idea. Like with the previous quotes and examples, liberal assumptions are made, rather than a true simulation of the laws involved.