Holistic projection of initial conditions onto a finite difference approximation

DOI10.1016/S0010-4655(01)00359-9zbMath0991.65138arXivmath/0101205OpenAlexW1975342024WikidataQ127809405 ScholiaQ127809405MaRDI QIDQ5956360

Anthony Roberts

Publication date: 1 September 2002

Published in: Computer Physics Communications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0101205

zbMATH Keywords

dynamical systemsKuramoto-Sivashinsky equationinitial conditionBurger's equationcentre manifoldholistic finite differences

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15)

Related Items (2)

Resolution of subgrid microscale interactions enhances the discretisation of nonautonomous partial differential equations ⋮ Resolving the Multitude of Microscale Interactions Accurately Models Stochastic Partial Differential Equations

Cites Work

• Applications of centre manifold theory
• Low-dimensional modelling of dynamics via computer algebra
• Computer algebra derives correct initial conditions for low-dimensional dynamical models
• Holistic discretization ensures fidelity to Burgers' equation

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