Numerical methods for solution of the stochastic differential equations equivalent to the non-stationary Parker's transport equation
arXiv:1509.06890 · doi:10.1088/1742-6596/633/1/012058
Abstract
We derive the numerical schemes for the strong order integration of the set of the stochastic differential equations (SDEs) corresponding to the non-stationary Parker transport equation (PTE). PTE is 5-dimensional (3 spatial coordinates, particles energy and time) Fokker- Planck type equation describing the non-stationary the galactic cosmic ray (GCR) particles transport in the heliosphere. We present the formulas for the numerical solution of the obtained set of SDEs driven by a Wiener process in the case of the full three-dimensional diffusion tensor. We introduce the solution applying the strong order Euler-Maruyama, Milstein and stochastic Runge-Kutta methods. We discuss the advantages and disadvantages of the presented numerical methods in the context of increasing the accuracy of the solution of the PTE.
4 pages, 2 figures, presented on 4th International Conference on Mathematical Modeling in Physical Sciences, 2015