Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8053593 | Applied Mathematics Letters | 2018 | 10 Pages |
Abstract
It is well known that for gradient systems in Euclidean space or on a Riemannian manifold, the energy decreases monotonically along solutions. In this letter we derive and analyse functionally fitted energy-diminishing methods to preserve this key property of gradient systems. It is proved that the novel methods are energy-diminishing and can achieve damping for very stiff gradient systems. We also show that the methods can be of arbitrarily high order and discuss their implementations. A numerical test is reported to illustrate the efficiency of the new methods in comparison with three existing numerical methods in the literature.
Keywords
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Physical Sciences and Engineering
Engineering
Computational Mechanics
Authors
Bin Wang, Ting Li, Yajun Wu,