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Analogues of Kahan's method for higher order equations of higher degree
Kahan introduced an explicit method of discretization for systems of for...
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Formal Power Series Solutions of First Order Autonomous Algebraic Ordinary Differential Equations
Given a first order autonomous algebraic ordinary differential equation,...
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Word-series high-order averaging of highly oscillatory differential equations with delay
We show that, for appropriate combinations of the values of the delay an...
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Order conditions for sampling the invariant measure of ergodic stochastic differential equations on manifolds
We derive a new methodology for the construction of high order integrato...
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Strapdown Attitude Computation: Functional Iterative Integration versus Taylor Series Expansion
This paper compares two basic approaches to solving ordinary differentia...
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Guaranteed convergence for a class of coupled-cluster methods based on Arponen's extended theory
A wide class of coupled-cluster methods is introduced, based on Arponen'...
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Positivity-preserving methods for population models
Many important applications are modelled by differential equations with ...
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Order theory for discrete gradient methods
We present a subclass of the discrete gradient methods, which are integrators designed to preserve invariants of ordinary differential equations. From a formal series expansion of the methods, we derive conditions for arbitrarily high order. We devote considerable space to 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 applied to the Hénon-Heiles system and a Lotka-Volterra system.
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