Abstract
We present numerical solutions to both the standard and modified two-dimensional Fokker-Planck equations with adiabatic focusing and isotropic pitch-angle scattering. With the numerical solution of the particle distribution function, we then discuss the related numerical issues, calculate the parallel diffusion coefficient using several different methods, and compare our numerical solutions for the parallel diffusion coefficient to the analytical forms derived earlier. We find the numerical solution to the diffusion coefficient for both the standard and modified Fokker-Planck equations agrees with that of Shalchi for the mean squared displacement method of computing the diffusion coefficient. However, we also show the numerical solution agrees with that of Litvinenko and Shalchi & Danos when calculating the diffusion coefficient via the velocity correlation function.
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