Arbitrary-order functionally fitted energy-diminishing methods for gradient systems

作者：Wang, Bin^*; Li, Ting; Wu, Yajun

来源：Applied Mathematics Letters, 2018, 83: 130-139.

DOI：10.1016/j.aml.2018.03.026

• Gradient systems
• Energy-diminishing methods
• Functionally fitted methods
• Arbitrary-order methods

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.

• 出版日期2018-9
• 单位曲阜师范大学