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- W2123661072 abstract "For gradient systems in Euclidean space or on a Riemannian manifold the energy decreases monotoni-cally along solutions. Algebraically stable Runge–Kutta methods are shown to also reduce the energyin each step under a mild step size restriction. In particular, Radau IIA methods can combine energymonotonicity and damping in stiff gradient systems. Discrete-gradient methods and averaged vector fieldcollocation methods are unconditionally energy-diminishing, but cannot achieve damping for very stiffgradient systems. The methods are discussed when they are applied to gradient systems in local coordi-nates as well as for manifolds given by constraints.Keywords: Gradient flow, energy dissipation, implicit Runge–Kutta method, algebraic stability, L-stability, discrete-gradient method, averaged vector field collocation." @default.
- W2123661072 created "2016-06-24" @default.
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- W2123661072 date "2013-10-03" @default.
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- W2123661072 title "Energy-diminishing integration of gradient systems" @default.
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- W2123661072 doi "https://doi.org/10.1093/imanum/drt031" @default.
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