Abstract
A proof is outlined showing that a fourth order exponentially fitted method isA-stable provided that the fitting parameterQ satisfiesQ≦z06≈ −4.12779 wherez06 is the negative root of the equation $$\exp (Q)(2Q^4 + 3Q^3 - 18Q^2 + 72) + (Q^4 + 3Q^3 - 18Q^2 - 72Q - 72) = 0.$$
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