A holistic finite difference approach models linear dynamics consistently

DOI10.1090/S0025-5718-02-01448-5zbMath1008.37047arXivmath/0003135MaRDI QIDQ4780371

Anthony Roberts

Publication date: 19 November 2002

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0003135

zbMATH Keywords

perturbationsnonlinear partial differential equationsgrid spacingcentre manifold approach

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Special approximation methods (nonlinear Galerkin, etc.) for infinite-dimensional dissipative dynamical systems (37L65) Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems (37L10) Approximation methods and numerical treatment of dynamical systems (37M99)

Related Items (9)

Smooth subgrid fields underpin rigorous closure in spatial discretisation of reaction-advection-diffusion PDEs ⋮ Adaptively Detect and Accurately Resolve Macro-scale Shocks in an Efficient Equation-Free Multiscale Simulation ⋮ Good coupling for the multiscale patch scheme on systems with microscale heterogeneity ⋮ Choose inter-element coupling to preserve self-adjoint dynamics in multiscale modelling and computation ⋮ Resolution of subgrid microscale interactions enhances the discretisation of nonautonomous partial differential equations ⋮ A dynamical systems approach to simulating macroscale spatial dynamics in multiple dimensions ⋮ Accuracy of Patch Dynamics with Mesoscale Temporal Coupling for Efficient Massively Parallel Simulations ⋮ Holistic discretization ensures fidelity to Burgers' equation ⋮ Resolving the Multitude of Microscale Interactions Accurately Models Stochastic Partial Differential Equations

Cites Work

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• Nonlinear Galerkin Methods
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• Holistic discretization ensures fidelity to Burgers' equation

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