DIVPAG solves an initial-value problem for ordinary differential equations using the ABM ODE solver method described previously.
Illustration of how the predictor - corrector ODE solver moves forward in a timestep. Values in the XX vector (only one element or vector illustrated) are interpolated to give an estimate of the XX element at the current time-step (prediction). The XX vector is then also used to calculate, along with the associated forces on the vessel, the corresponding rates of change of the XX values (DXDT). Integration of the DXDT values then produces a corresponding value at the current time-step (the correction). If the predicted and corrected values lie within a tolerance level then the solution moves forward in time. If they do not agree a the solver reduces the time-step and recalculates. This process is continued until there is agreement between the predicted and corrected values.
Almost there now.