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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 .
The early identification of self-similar solutions of the second kind can be found in problems of imploding shock waves (Guderley–Landau–Stanyukovich problem), analyzed by G. Guderley (1942) and Lev Landau and K. P. Stanyukovich (1944), [3] and propagation of shock waves by a short impulse, analysed by Carl Friedrich von Weizsäcker [4] and ...
The Euler three-body problem is known by a variety of names, such as the problem of two fixed centers, the Euler–Jacobi problem, and the two-center Kepler problem. The exact solution, in the full three dimensional case, can be expressed in terms of Weierstrass's elliptic functions [ 2 ] For convenience, the problem may also be solved by ...
For example, the shooting method (and its variants) or global methods like finite differences, [3] Galerkin methods, [4] or collocation methods are appropriate for that class of problems. The Picard–Lindelöf theorem states that there is a unique solution, provided f is Lipschitz-continuous .
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt to find approximate solutions of problems rather than the exact ones.
When we recently wrote about the toughest math problems that have been solved, we mentioned one of the greatest achievements in 20th-century math: the solution to Fermat’s Last Theorem. Sir ...
In mathematics, the Simon problems (or Simon's problems) are a series of fifteen questions posed in the year 2000 by Barry Simon, an American mathematical physicist. [ 1 ] [ 2 ] Inspired by other collections of mathematical problems and open conjectures, such as the famous list by David Hilbert , the Simon problems concern quantum operators . [ 3 ]
The following is a list of notable unsolved problems grouped into broad areas of physics. [1]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.