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Arbitrary-order functionally fitted energy-diminishing methods for gradient systems. (arXiv:1801.08484v1 [math.NA])
来源于:arXiv
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 unconditionally 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. 查看全文>>