Papers › Order theory for discrete gradient methods
Order theory for discrete gradient methods
Sølve Eidnes
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The discrete gradient methods are integrators designed to preserve invariants of ordinary differential equations. From a formal series expansion of a subclass of these methods, we derive conditions for arbitrarily high order. We derive specific results for the average vector field discrete gradient, from which we get P-series methods in the general case, and B-series methods for canonical Hamiltonian systems. Higher order schemes are presented, and their applications are demonstrated on the H\'enon-Heiles system and a Lotka-Volterra system, and on both the training and integration of a pendulum system learned from data by a neural network.
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