Statistics – Computation
Scientific paper
Jan 1996
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996gmu..rept.....b&link_type=abstract
Technical Report, George Mason Univ. Fairfax, VA United States
Statistics
Computation
Computational Astrophysics, Differential Equations, Gamma Rays, Space Plasmas, Time Dependence, Integral Equations, Mathematical Models, X Rays, Compton Effect, Algorithms, Electron Mobility, Perturbation, Photons
Scientific paper
The research performed under the above titled ONR grant has resulted in a number of important advances in the treatment of integrodifferential transport equations, such as those obtained when the Fokker-Planck coefficients depend on the temperature of the particle distribution, as defined by a suitable integral. In summary, we have developed a new technique for independently determining the temperature as a function of time using the energy moments of the initial distribution. This is equivalent to decoupling the original integrodifferential problem into two parts: (1) determination of the temperature variation, and (2) determination of the particle distribution as a function of time and energy. This represents a major advance in the treatment of integrodifferential Fokker-Planck equations because the two problems obtained can be solved separately without recourse to traditional predict or corrector algorithms. The technique has been applied with success to the problem of self-consistent Comptonization in astrophysical plasmas. The theoretical approach utilizes a novel combination of physics, applied mathematics, and advanced symbolic computational techniques, and shows good promise for generalization to the treatment of other integrodifferential systems of interest to the Navy. The multi-disciplinary CSI program at George Mason University has proven an ideal venue for this investigation.
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