A new class of highly-stable methods:A0-stable methods
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A linear multistep method (ζ,σ) is defined to beA0-stable if when it is applied to the equation\(\dot x(t) = - \lambda x(t)\) the approximate solutionx h (t n ) tends to zero ast n → ∞ for all values of the stepsizeh and allλ∈(0, ∞).
Various properties ofA0-stable methods are derived. It is shown that most of the properties ofA(α)-stable methods are shared byA0-stable methods. It is proved that there existA0-stable methods of arbitrarily high order.
KeywordsComputational Mathematic Stable Method Multistep Method Linear Multistep Method
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