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2.3.2 Stiff Problems: Backward Differentiation Formulas

A problem is stiff if the numerical solution has its step size limited more severely by the stability of the numerical technique than by the accuracy of the technique. Frequently, these problems occur in systems of differential equations that involve several components that are decaying at widely differing rates. The reader is encouraged to consult the excellent survey article [6] by Shampine and Gear, ``A User's View of Solving Stiff Ordinary Differential Equations.''

A simple scalar example of stiffness is given by C.W. Gear [5]:

where is a smooth, slowly varying function. The solution,

has a component that will be insignificant compared to for t sufficiently large. The numerical method, however, will always have its step size h limited by the magnitude of for the entire integration.