Mathematics – Probability
Scientific paper
Jan 1987
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987a%26a...172..350h&link_type=abstract
Astronomy and Astrophysics (ISSN 0004-6361), vol. 172, no. 1-2, Jan. 1987, p. 350-358. Research supported by the Space Research
Mathematics
Probability
8
Cosmic Rays, Diffusion, Maximum Entropy Method, Approximation, Differential Equations, Probability Density Functions
Scientific paper
A method is described for obtaining approximate solutions to a differential equation involving a density function in accordance with Jaynes' principle of maximum entropy. The method uses some known moments of the real solution, obtained directly from the differential equation. Jaynes' principle provides a criterion necessary to construct from these moments an approximation to the real solution. After some introductory examples, the maximum entropy method is applied to simple forms of the cosmic ray transport equation. The resulting approximation, as well as the familiar diffusion approximation, are compared with a numerical solution. It is found that there is qualitative agreement between the maximum entropy approximation and the numerical solution, and that the method is a significant improvement on the diffusion approximation, especially in its description of first order anisotropy.
Hick Pierre P.
Stevens Gary
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