Abstract
Time evolutions of certain spherically symmetric systems are investigated where simple explicit second order finite difference methods are not applicable. Due to a compactified space coordinate, efficiency and long-term numerical stability require at least fourth order accuracy for both the massive Klein–Gordon field and the SU(2) Yang–Mills–Higgs system. Moreover, adaptive mesh refinement (AMR) has a crucial role in dealing with high frequency oscillations that appear as an initial disturbance is radiated away. The incompatibility of AMR with fully fourth order accuracy is discussed and a solution is presented. Finally, compactification is compared to standard spherical coordinates and truncated grids in terms of efficiency.
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