What is considered a stiff ordinary differential equation (ODE) in MATLAB 8.0 (R2012b)?

I would like to know what a stiff ordinary differential equation is.

Answer 1

[MathWorks Support Team]

There is no agreed upon definition.

ODEs have been called stiff if one or more of the following is true:

• The ODE cannot be solved by an explicit method in a reasonable amount of time.
• The solution of the ODE can be expressed as the sum of highly oscillatory and/or transient solutions and other more slowly changing components.
• The ODE must be solved with an implicit method.
• The ODE has a large stiffness ratio.

Consider the ODE:

 y' = f(t,y)

 y(0) = y0

In some definitions, the stiffness of the ODE depends on the function f and initial conditions y0. In others, stiffness depends only on the function f.