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In contrast to single-step methods, an additional stability property is required for the asymptotic convergence of multistep methods, which ensures the boundedness of numerical solutions. This condition can be assessed by considering the eigenvalues of the companion matrix of a multistep method.

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Convergence of Multistep Methods

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  • 发表日期：

    2025年

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  • Sören Bartels

摘要

In contrast to single-step methods, an additional stability property is required for the asymptotic convergence of multistep methods, which ensures the boundedness of numerical solutions. This condition can be assessed by considering the eigenvalues of the companion matrix of a multistep method.