On the symmetrization and composition of nonstandard finite difference schemes as an alternative to Richardson's extrapolation
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On the symmetrization and composition of nonstandard finite difference schemes as an alternative to Richardson's extrapolationData de publicació
2022-04-29Editor
Taylor and Francis Group; Taylor and FrancisISSN
1023-6198; 1563-5120Cita bibliogràfica
CALATAYUD, Julia; JORNET, Marc. On the symmetrization and composition of nonstandard finite difference schemes as an alternative to Richardson's extrapolation. Journal of Difference Equations and Applications, 2022, p. 1-9.Tipus de document
info:eu-repo/semantics/articleVersió
info:eu-repo/semantics/acceptedVersionParaules clau / Matèries
Resum
From the classical explicit Euler scheme of first order, nonstandard finite difference (NSFD) schemes were envisioned to mimic the essential properties of the governing differential equation model for every time ... [+]
From the classical explicit Euler scheme of first order, nonstandard finite difference (NSFD) schemes were envisioned to mimic the essential properties of the governing differential equation model for every time step-size. In the context of compartmental epidemiological models, these properties are generally concerned with the positivity of subpopulations, conservation laws (dynamics of the total population), and stability. However, for autonomous systems, the symmetry (self-adjoint) condition is not preserved. Compartmental epidemiological models are Poisson systems, so methods from geometric numerical integration should be applicable. It is found that symmetrization of NSFD schemes does not respect positivity for every step-size, though other characteristics are maintained and second order is reached. Composition through the Lie formalism can then be applied to obtain higher-order schemes. This is a more efficient and consistent alternative to Richardson's extrapolation, which has often been used to go beyond order one. [-]
Publicat a
Journal of Difference Equations and Applications. Volume 28, 2022 - Issue 5Entitat finançadora
Universitat Jaume I
Codi del projecte o subvenció
UJI-B2019-17
Drets d'accés
info:eu-repo/semantics/openAccess
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