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

MATLABodestiffstiffnes

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

Best Answer

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.
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