A-stability
The behaviour of numerical methods on stiff problems can be analyzed by applying these methods to the test equation y' = ky subject to the initial condition y(0) = 1 with . The solution of this equation is y (t) = ekt. This solution approaches zero as when If the numerical method also exhibits this behaviour, then the method is said to be A-stable. A-stable methods do not exhibit the instability problems as described in the motivating example.
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