Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Arbitrary-order functionally fitted energy-diminishing methods for
  gradient systems   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.

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The categories of this paper are: nucl-th
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The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: q-fin
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The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat