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Computational physics is the study and implementation of numerical analysis to solve problems in physics. [1] Historically, computational physics was the first application of modern computers in science, and is now a subset of computational science .
Some of the major unsolved problems in physics are theoretical, meaning that existing theories seem incapable of explaining a certain observed phenomenon or experimental result. The others are experimental, meaning that there is a difficulty in creating an experiment to test a proposed theory or investigate a phenomenon in greater detail.
The three-body problem is a special case of the n-body problem, which describes how n objects move under one of the physical forces, such as gravity. These problems have a global analytical solution in the form of a convergent power series, as was proven by Karl F. Sundman for n = 3 and by Qiudong Wang for n > 3 (see n-body problem for details
The sign problem is one of the major unsolved problems in the physics of many-particle systems, impeding progress in many areas: Condensed matter physics — It prevents the numerical solution of systems with a high density of strongly correlated electrons, such as the Hubbard model. [1]
Nowadays inverse problems are also investigated in fields outside physics, such as chemistry, economics, and computer science. Eventually, as numerical models become prevalent in many parts of society, we may expect an inverse problem associated with each of these numerical models.
In many-body physics, the problem of analytic continuation is that of numerically extracting the spectral density of a Green function given its values on the imaginary axis. It is a necessary post-processing step for calculating dynamical properties of physical systems from Quantum Monte Carlo simulations, which often compute Green function ...
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Numerical relativity is one of the branches of general relativity that uses numerical methods and algorithms to solve and analyze problems. To this end, supercomputers are often employed to study black holes , gravitational waves , neutron stars and many other phenomena described by Albert Einstein's theory of general relativity .