Numerical methods for solution of the stochastic differential equations equivalent to the non-stationary Parker's transport equation [SSA]

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.

Read this paper on arXiv…

A. Wawrzynczak, R. Modzelewska and M. Kluczek
Thu, 24 Sep 15

Comments: 4 pages, 2 figures, presented on 4th International Conference on Mathematical Modeling in Physical Sciences, 2015