Comparative Analysis of Numerical Methods for Strong Order Integration of Stochastic Differential Equations in Galactic Cosmic Ray Particle Transport

Project Description:

The objective of this project is to perform a comprehensive comparative analysis of numerical methods used for the strong order integration of stochastic differential equations (SDEs) in the context of the non-stationary Parker transport equation (PTE). The PTE, a Fokker-Planck type equation, describes the non-stationary transport of galactic cosmic ray (GCR) particles in the heliosphere, encompassing three spatial coordinates, particle energy, and time. The project aims to investigate the following: 1. Numerical Methods: Evaluate and compare the performance of key numerical schemes including the Euler-Maruyama, Milstein, and stochastic Runge-Kutta methods for the integration of SDEs associated with the PTE. Assess their accuracy, efficiency, and stability in capturing the dynamic behavior of GCR particle transport. 2. Characteristic Analysis: Analyze the subtle differences observed in the trajectories, rigidity, and exit time of pseudoparticles generated by the tested numerical schemes. Examine the impact of these differences on the final spectrum of the particle distribution. 3. Detailed Examination: Conduct a detailed analysis of the pseudoparticle characteristics and assess their significance in the context of GCR particle transport. Investigate the potential implications of the observed variations on the understanding of particle dynamics and the overall accuracy of the numerical methods.

Research Area:

Space Physics

Project Level:

Masters

This Project Is Offered At The Following Node(s):

(UCT)(UKZN)(NWU)