Methods, computer systems, and computer readable media are provided for simulation of a model of a system by detecting a violation of a cross condition while iteratively refining a first solution of a system of nonlinear algebraic equations at a current time point, and responsive to the detecting, predicting a crossing time step, projecting an initial guess for a second solution of the system of nonlinear algebraic equations at the crossing time point, and iteratively refining the second solution and the crossing time step by jointly solving an equation for the cross condition with the system of nonlinear algebraic equations as a coupled nonlinear system in which the crossing time step is treated as an unknown to compute changes to the second solution and the crossing time step in each iteration.