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A-Stability


A-stability is the property of a numerical method for ordinary differential equations that its stability region contains the entire left half-plane. Equivalently, when the method is applied to the test equation y^'=lambday, it is stable for every step size h>0 whenever Relambda<0, so hlambda lies in the left half-plane.

For example, the Euler backward method is A-stable, whereas the Euler forward method is not.


See also

Euler Backward Method, Euler Forward Method, Stability Region

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References

Hairer, E. and Wanner, G. Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems, 2nd ed. Berlin, Germany: Springer-Verlag, 1996.

Cite this as:

Weisstein, Eric W. "A-Stability." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/A-Stability.html

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