Fourth order AMR and nonlinear dynamical systems in compactified space

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.