Arbitrary-order functionally fitted energy-diminishing methods for gradient systems
Numerical Analysis
2018-04-17 v1
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 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.
Keywords
Cite
@article{arxiv.1801.08484,
title = {Arbitrary-order functionally fitted energy-diminishing methods for gradient systems},
author = {Bin Wang and Ting Li and Yajun Wu},
journal= {arXiv preprint arXiv:1801.08484},
year = {2018}
}