A Picard Iteration Based Integrator

converge to a unique solution of the IVP up to the boundary of U [1]. In general, φn may converge slowly to the exact solution. The Picard iteration based integrator described in this paper has three main advantages. The the integrator has arbitrary order, is time adaptive, and has dense output. Dense output refers to the integrator being able to take time steps of variable length without having to recompute previous steps. These advantages are intertwined to balance local truncation error with computational efficiency. When smaller time steps are required, the order can be reduced to maintain efficiency. When a larger time step is appropriate, the order can be increased to maintain lower local truncation error. The advantages of the integrator make it well suited for modelling the motion of charged particles. The forces in Coulomb interactions are proportional to the inverse of the square of the distances between particles. There are situations such as when two particles with same signed charges are on a near collision course. If too large of a time step is taken, the large repulsive force between the particles as they move closer to one another may not be considered and the integrator will give physically unrealistic results. An integrator with dense output can avoid these errors.