Dissipativity of Runge-Kutta methods in Hilbert spaces

被引：0

作者：

Adrian T. Hill

机构：

[1] University of Bath,School of Mathematical Sciences

来源：

BIT Numerical Mathematics | 1997年 / 37卷

关键词：

65L07; 34D05; Runge-Kutta Methods; nonlinear stability; dissipativity;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

This paper concerns the discretization by Runge-Kutta methods of the initial value problemut=f(u), under the dissipative structural condition that there exist α≥0, β>0, such thatf:W→H, ℜe, ∀w∈W, for complex Hilbert spacesW⊆H. It is shown that strong A-stability is necessary to ensure the dissipativity of the method, whilst algebraic stability plus |R(∞)|<1 is a sufficient condition in the case of DJ-irreducible methods.

引用

页码：37 / 42

页数：5

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[6]

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[7]

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