Holistic discretization ensures fidelity to Burgers' equation

DOI10.1016/S0168-9274(00)00053-2zbMath0984.65090OpenAlexW2036425975WikidataQ127351906 ScholiaQ127351906MaRDI QIDQ5937478

Anthony Roberts

Publication date: 14 May 2002

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0168-9274(00)00053-2

zbMATH Keywords

stabilityaccuracyBurgers' equationcenter manifold theorycomputer algebra program

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12)

Related Items (9)

A holistic finite difference approach models linear dynamics consistently ⋮ Smooth subgrid fields underpin rigorous closure in spatial discretisation of reaction-advection-diffusion PDEs ⋮ 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 projection of initial conditions onto a finite difference approximation ⋮ Resolving the Multitude of Microscale Interactions Accurately Models Stochastic Partial Differential Equations

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