Tackling stiffness in process simulations the properties of a stiff integration algorithm

8 Tackling stiffness in process simulations the properties of a stiff integration algorithm 

These restrictions cause us to consider implicit algorithms as an alternative. 

To illustrate the difference in stability properties between explicit and implicit integration algorithms, consider again the equation used to describe valve dynamics in Section 2.2. Dropping the subscripts from equation (2.9) for clarity and generality, and setting the demanded valve travel, xj, to zero, indicating a 

However, the implicit, backward Euler approximation gives 

From inspection, this is stable for all positive values of the timestep. At, in-line with Dahlquist. 

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