In order to answer the question of stiff ODEs, let's look at an example in

*A First Course in the Numerical Analysis of Differential Equations*by Iserles [**1**].
Hoffman [

**2**] states that stiffness appears for**single****linear**and**nonlinear**ODEs,**higher-order****linear**and**nonlinear**ODEs, and**systems**of**linear**and**nonlinear**ODEs. He lists several deﬁnitions for stiﬀness:**1.**An ODE is stiﬀ if the step size required for stability is much smaller than the step size required for accuracy.

**2.**An ODE is stiﬀ if it contains some components of the solution that decay rapidly compared to other components of the solution.

**3.**A system of ODEs is stiﬀ if at least one eigenvalue of the system is negative and large compared to the other eigen values of the system.

**4.**From a practical point of view, an ODE is stiﬀ if the step sixe based on cost (i.e., computational time) is too large to obtain an accurate (i.e., stable) solution.

Hoﬀman [

**2**] also gives a couple of examples.
In progress...to be continued.

**References**:

[

**1**] A. Iserles.*A First Course in the Numerical Analysis of Diﬀerential Equations*. 2nd ed. Cambridge University Press, Cambridge, UK. 2009
[

**2**] J. D. Hoﬀman.*Numerical Methods for Engineers and Scientists*. 2nd ed. Marcel Dekker, Inc., New York, NY. 2001
## No comments:

## Post a Comment