A Global Newton-like Method

All methods considered in the previous subsections rely on successive 

The object of this subsection consists in solving Eq.(3) by an associated differential equation. There are several ways to do this. 

The differential Eq.(54a) represents Newton s second law (with a dissipative force) and so the solution curves have a physically meaning within a semi classical framework. This question is discussed in detail in Ref.55. 

It is easy to verify that each stationary point x of E corresponds 

For a better understanding of the mathematical background method, a little excursion to the stability theory of differential equations is useful. To this end we consider the first order differential equation 

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