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The problem of solving for charged particle dynamics under the influence of electromagneticfields is a fundamental component of particle simulation models to simulate plasma physics. This task - known as the particle pushing problem - is especially challenging when the plasma is strongly magnetized due to numerical stiffness arising from the wide range of time scales between highly oscillatory gyromotion and long term macroscopic behavior of the system, thus calling for computationally efficient numerical methods.

This dissertation investigates an alternative approach to numerically simulate strongly magnetized charged particle dynamics using exponential integration techniques. We first derive exponential integrators to solve strongly magnetized particle pushing problems and implement a novel algorithm to evaluate matrix φ functions that is computationally efficient for low dimensional problems. We then extend this work by deriving Nytröm type exponential integrators that effectively solve the particle pushing problem in its second-order form directly. Numerical experiments comparing these exponential integrators against two conventional particle pushing algorithms demonstrate that exponential integrators are superior for linear and weakly nonlinear problems and are competitive for nonlinear problems. In particular, the Nyström type exponential integrators exhibit significant computational savings over the standard exponential integrators. These results demonstrate that exponential integrators are a promising alternative to numerically solve strongly magnetized particle pushing problems.