Stff System

I am very new to Julia
While solving ODE i have come across Stiff system
Wat does the Stiff system means.

The concept of stiff ordinary differential equations is not particularly Julia-specific, it is general. Loosely speaking, stiff ODEs model both fast and slow dynamics. For example, your ODEs model both the dynamics of a heavy mechanical robotic arm and the dynamics of an electronic motor driver. Time responses of the two easily differ in orders of magnitude.

This property constitutes a challenge for algorithms that are not specialized for such systems, typically explicit solvers such as the popular (explicit) Runge-Kutta methods. The fast dynamics call for a short integration step, othewise stability of the solver is lost. But slow dynamics require a long simulation interval. As a consequence, a huge number of integrations steps is needed to accomplish the simulation. What you observe in such situations is that the simulation slows down horribly, it looks as if it stalled completely, and yet it moves on. Efficiency issue. Specialized solvers for stiff problems (in fact, implicit solvers) are insensitive to such problems and the simulation flies with them (on nonstiff problems they are rather more computationally demanding, that is why you do not want to use them for nonstiff problems).

You may want to have a look at the following description or Well, the examples are prepared using Matlab but the general description is relevant for Julia as well. For a full treatment, you may want to consult the classic by Hairer and Wanner.


Thank You Professor
Concept was more cleared by your explanation.

1 Like