Stability Analysis of a Nonlinear DiffusionType Kinetic Equation
Abstract
A diffusiontype partial differential equation with nonlinear coefficients is analysed for stability in the von Neumann sense, and some numerical examples are given. The equation is a kinetic equation representing an instantaneous injection of energetic photons into a thermalised cosmological background radiation (CBR) and the subsequent time evolution of the electromagnetic spectrum. Compton, double Compton, and bremsstrahlung are the only interactions considered at the relatively photon energies low. The final conservative, implicit, finite difference scheme is a refinement of a similar model developed by Lightman, which is shown to be not stable for some cases considered. A semiLagrangian modification is used to account for the expansion of the universe. The full physical derivation of the kinetic equation and the associated parameters are given elsewhere.
 Publication:

Journal of Computational Physics
 Pub Date:
 June 1992
 DOI:
 10.1016/00219991(92)90233O
 Bibcode:
 1992JCoPh.100..253G