Locally Exact Integrators for the Duffing Equation

Autor:	Jan L. Cieśliński, Artur Kobus
Jazyk:	angličtina
Rok vydání:	2020
Předmět:	geometric numerical integration exact discretization locally exact methods discrete gradient method linear gradient form of odes dissipative systems Mathematics QA1-939
Zdroj:	Mathematics, Vol 8, Iss 2, p 231 (2020)
Druh dokumentu:	article
ISSN:	2227-7390
DOI:	10.3390/math8020231
Popis:	A numerical scheme is said to be locally exact if after linearization (around any point) it becomes exact. In this paper, we begin with a short review on exact and locally exact integrators for ordinary differential equations. Then, we extend our approach on equations represented in the so called linear gradient form, including dissipative systems. Finally, we apply this approach to the Duffing equation with a linear damping and without external forcing. The locally exact modification of the discrete gradient scheme preserves the monotonicity of the Lyapunov function of the discretized equation and is shown to be very accurate.
Databáze:	Directory of Open Access Journals
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