On the symmetrization and composition of nonstandard finite difference schemes as an alternative to Richardson's extrapolation
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Title
On the symmetrization and composition of nonstandard finite difference schemes as an alternative to Richardson's extrapolationDate
2022-04-29Publisher
Taylor and Francis Group; Taylor and FrancisISSN
1023-6198; 1563-5120Bibliographic citation
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.Type
info:eu-repo/semantics/articleVersion
info:eu-repo/semantics/acceptedVersionSubject
Abstract
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. [-]
Is part of
Journal of Difference Equations and Applications. Volume 28, 2022 - Issue 5Funder Name
Universitat Jaume I
Project code
UJI-B2019-17
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info:eu-repo/semantics/openAccess
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- MAT_Articles [766]