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 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.
Highlights
We employ the stochastic methodology to model the galactic cosmic rays (GCR) transport in the heliosphere
Transport of the GCR particles in the heliosphere can be described by the Parker transport equation [1]:
We have presented [2] that the GCR transport can be effectively modelled based on the solution of the set of stochastic differential equations (SDEs) corresponding to the Parker transport equation (PTE) (1)
Summary
We employ the stochastic methodology to model the galactic cosmic rays (GCR) transport in the heliosphere. We have presented [2] that the GCR transport can be effectively modelled based on the solution of the set of stochastic differential equations (SDEs) corresponding to the PTE (1). The PTE must be brought to the form of the backward Fokker-Planck equation (e.g.[3]), and the corresponding SDEs must be solved numerically.
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