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We derive the numerical schemes for the strong order integration of the setof the stochastic differential equations (SDEs) corresponding to thenon-stationary Parker transport equation (PTE). PTE is 5-dimensional (3 spatialcoordinates, particles energy and time) Fokker- Planck type equation describingthe non-stationary the galactic cosmic ray (GCR) particles transport in theheliosphere. We present the formulas for the numerical solution of the obtainedset of SDEs driven by a Wiener process in the case of the fullthree-dimensional diffusion tensor. We introduce the solution applying thestrong order Euler-Maruyama, Milstein and stochastic Runge-Kutta methods. Wediscuss the advantages and disadvantages of the presented numerical methods inthe context of increasing the accuracy of the solution of the PTE.

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