Benchmark C05 Two State Model deals with dis-continuities in dynamic systems. While the solution itself is continuous, the derivatives may have jumps, depending on thresholds for the states. Basis is a linear stiff system with two states, where parameters in the derivative function switch depending on threshold values for the state – resulting in rare switching or in high frequency switching. In any case, the switching time instants must be detected with high accuracy.

The task requires parameter variations resulting in drastically increasing number of switching, and validation of certain switching time instants with data from analytical solutions, and investigations on dependence of solutions on relative accuracy.

For education, this benchmark is suitable for getting knowledge in handling state events and mastering numerical and accuracy problems caused by stiff systems. Furthermore, numerical and analytical solutions can be compared, also for validation.